COLLECTED PAPERS

IN

PHYSICS AND ENGINEERING

CAMBRIDGE UNIVERSITY PRESS

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COLLECTED PAPERS

IN

PHYSICS AND ENGINEERING

BY
JAMES THOMSON, D.Sc., LL.D., F.R.S.

PROFESSOR OF ENGINEERING IN QUEEN'S COLLEGE, BELFAST
AND AFTERWARDS IN THE UNIVERSITY OF GLASGOW

SELECTED AND ARRANGED WITH UNPUBLISHED MATERIAL
AND BRIEF ANNOTATIONS BY

SIR JOSEPH LARMOR, D.Sc., LL.D., SEC. R.S., M.P.

LUCASIAN PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF CAMBRIDGE

AND

JAMES THOMSON, M.A.

Cambridge :

at the University Press

1912

PRINTED BY JOHN CLAY, M.A.
AT THE UNIVERSITY PRESS

PEBFACE

TT is well known — chiefly through references to his work by
- other physicists such as his brother Lord Kelvin, Thomas
Andrews, James Clerk Maxwell, Osborne Reynolds, J. Willard
Gibbs — that the scientific activity of James Thomson has left
permanent marks on the history of several branches of physical
science. The collection into readily accessible form, in one
volume, of his published contributions to knowledge, has thus
been desirable, especially in view of the scattered local journals,
often remote from modern facilities for reference, in which much
of the work originally appeared. The project of a posthumous
collection of his brother's work was constantly encouraged and
looked forward to by Lord Kelvin during his later years, but his
numerous pre-occupations prevented active assistance.

On the recent completion of the Collected Edition of Lord
Kelvin's own scientific work, the idea has impressed itself on
others that there should be available a full record of the work —
very different in general type from his own — of his brother who
was his lifelong companion and scientific associate. The materials
for the present collection have been brought together mainly by
the care of his son, James Thomson, of the Elswick Engineer-
ing Works, Newcastle-on-Tyne, assisted zealously by his wife who
has not survived to see the completion of her work; while the
Biographical Memoir, containing passages of high interest as
regards the personal aspect of the progress of Physical and
Engineering Science in this country in the middle of the last
century, has been constructed largely out of narratives and re-
collections obtained by his daughter Mary Hancock Thomson.

2G0987

VI PREFACE

Letters of scientific importance which passed between Lord Kelvin
and his brother, on subjects such as the Theory of the Dissipation
of Energy and the characteristics of natural flow in liquids, have
been included, as well as scientific correspondence with Faraday,
Clerk Maxwell, Andrews, H. C. Sorby and other eminent men.

The main characteristic of James Thomson's mind was the
marked originality of his way of looking at scientific problems,
arising in part perhaps from a combination, then more common
than now, of the abstract physical with the practical engineering
interest, but also fostered by the independent and unconventional
character of his scientific education. This quality was united
with singular persistence in brooding over a train of thought, and
following it out into all relevant details and ramifications. So
constantly was he pre-occupied with the various aspects of his
scientific problems, as to sometimes produce an impression that
his whole life was concentrated in one absorbing interest. But in
the published expression of his results, at any rate, he was usually
concise. The assemblage in 500 pages of so much pioneering
insight in so many subjects recalls in some respects the work of
even the most original of physicists. In many of these subjects
discovery and invention have of course progressed far beyond
what was feasible when these notes and papers were concerned
often with breaking almost new ground; the recent great develop-
ment of water-turbines for the electric utilization of hydraulic
power in mountainous regions is a case in point. But in the
main these papers are in no sense obsolete ; their acute direct
scrutiny of phenomena is of interest to the mathematical physicist
by way of contrast and supplement to his own procedure; and
where appositeness to practical application may have failed through
lapse of time, their relation to the history of science takes its
place.

Other examples of the topics treated in these papers may be
mentioned. In the first rank there is his own cardinal discovery
of the lowering of the freezing point by pressure, which ramifies
on one side into the subject of the influence of stress on solution
and crystallisation, and on the other into acute observations on the
formation of ice in nature, the ground ice of the St Lawrence, and

PREFACE vii

the glacial origin of the Parallel Roads of Glenroy. The investiga-
tions on the natural flow of water and its measurement are funda-
mental in the practical science of hydraulics. He also devoted
lifelong attention to the problems of the general atmospheric
circulation, summing up in the Bakerian Lecture compiled in the
last year of his life. Again, his close association as a colleague
with Thomas Andrews, at the time when the latter was occupied
by his classical researches on the continuity of the gaseous and
liquid states of matter, led them to the well-known developments
concerning the unstable regions in the Andrews diagram, on which
much new matter has now been added from unpublished manu-
scripts. The remarkable early papers on elasticity, on the influence
of intrinsic strain on the strength of materials, on the dynamics
of spiral springs, have remained prominent through Lord Kelvin's
expositions. In his later years the foundations of abstract
dynamics, in connexion with the fundamental characteristic of
relativity, led to fresh and original papers, which have regained
interest from the wider physical discussions now prevalent on that
subject.

The Editors desire to record their thanks for much valuable
assistance received, as regards the printing of the volume, from
the staff of the Cambridge University Press.

J. L.

CAMBRIDGE,
July 1912.

CONTENTS

PAGE

PREFACE v

CONTENTS ix

INTRODUCTORY AND BIOGRAPHICAL .... xiii

Obituary Notice by Dr J. T. Bottomley, F.R.S. . xcii
List of Scientific Terms introduced by Prof. James

Thomson ciii

PAPERS RELATING TO FLUID MOTION

YEAR No.

1852 1 On Some Properties of Whirling Fluids [Vertical Free
Vortex], with their Application in improving the
Action of Blowing Fans, Centrifugal Pumps, and
certain kinds of Turbines 1

1852 2 On the Vortex Water- Wheel 2

1855 3 On a Centrifugal Pump and Windmill erected for

Drainage and Irrigation in Jamaica ... 16

1858 4 On a Centrifugal Pump with Exterior Whirlpool, Con-
structed for Draining Land . . . . . 16

1855 5 On the Friction Break Dynamometer .... 24

1852 6 On a Jet Pump, or Apparatus for drawing up Water by

the Power of a Jet 26

1853 7 On an Experimental Apparatus constructed to deter-

mine the Efficiency of the Jet Pump ; and a Series

of Results obtained ...... 27

1855 8 On the Jet Pump and its Application to the Drainage

of Swampy Lands and Shallow Lakes ... 30
1864 9 On a New Application of the Jet Pump by Steam as

Auxiliary to a Large Drainage Centrifugal Pump 34

1855 10 On Practical Details of the Measurement of Running

Water by Weir-Boards 35

1858 11 On Experiments on the Measurement of Water by

Triangular Notches in Weir-Boards ... 36
1861 12 On Experiments on the Gauging of Water by Triangular

Notches 42

13 Table of Flow of Water in the Right- Angled V-Notch 54

X CONTENTS

YEAR No. PAGE

1876 14 Improved Investigatious on the Flow of Water through
Orifices with Objections to the Modes of Treatment
commonly adopted ....... 56

1876 15 On the "Vena Contracta" 88

1876 16 On the Origin of Windings of Rivers in Alluvial Plains,

with Remarks on the Flow of Water round Bends

in Pipes 96

1877 17 Experimental Demonstration in respect to the Origin

of Windings of Rivers in Alluvial Plains, and to
the Mode of Flow of Water round Bends of Pipes . 100
1879 18 On the Flow of Water round River Bends . . 102

1878 19 On the Flow of Water in Uniform Regime in Rivers

and other Open Channels ? 106

1888 20 On Flux and Reflux of Water in Open Channels or in

Pipes or other Ducts 123

1855 21 On certain curious Motions observable at the Surfaces

of Wine and other Alcoholic Liquors . . . 125

1868 22 On Smoky Fogs 130

1870 23 On Smoky Fogs (Second Paper) . , . . . . 133
1882 24 On a Changing Tesselated Structure in certain Liquids

[due to Convective Circulation] . . . . 136
1862 25 On the Cause of the Calm Lines often seen on a

Rippled Sea 142

1857 26 On the Grand Currents of Atmospheric Circulation . 144

1884 27 Whirlwinds and Waterspouts 148

1892 28 Bakerian Lecture.— On the Grand Currents of Atmo-
spheric Circulation . . . . . . . 153

CONGELATION AND LIQUEFACTION

1849 29 Theoretical Considerations on the Effect of Pressure

in Lowering the Freezing Point of Water . . 196

1850 30 The Effect of Pressure in Lowering the Freezing Point

of Water Experimentally Demonstrated. By Pro-
fessor William Thomson 204

1857 31 On the Plasticity of Ice, as manifested in Glaciers . 208

1858 32 Correspondence with Prof. Faraday on Regelation . 212
1862 33 On Tubular Pores in Ice Frozen on Still Water . 220

1859 34 On Recent Theories and Experiments regarding Ice at

or near its Melting point 222

1861 35 Note on Professor Faraday's Recent Experiments on

"Regelation" 230

1861 36 On Crystallization and Liquefaction, as influenced by

Stresses tending to Change of Form in the Crystals 236
1861 37 Correspondence with W. Thomson on the Influence of

Stress on Crystallization 245

CONTENTS xi

YEAK No. PAGE

1862 38 Correspondence with H. C. Sorby, F.R.S., on Geological

Effects of Pressure 252

1862 39 On the Disintegration of Stones exposed in Buildings

and otherwise to Atmospheric Influence . . 257

1862 40 On Ground or Anchor Ice and its Effects in the

St Lawrence 258

1864 41 On Conditions affording Freedom for Solidification to
Liquids which tend to Solidification, but experi-
ence a Difficulty of making a Beginning of their
Change of State 268

1864 42 Disintegration of Earth by Columnar Growth of Ice . 269

1888 43 Later Investigations on the Plasticity of Glacier Ice . 272

CONTINUITY OF STATES IN MATTER

1869 44 The Transition from the Liquid to the Gaseous State

in Matter 276

1871 45 Considerations on the abrupt change at Boiling or
Condensing in reference to the Continuity of the
Fluid State of Matter 278

1871 46 Speculations on the Continuity of the Fluid State of
Matter, and on Relations between the Gaseous, the
Liquid, and the Solid States (Brit. Assoc.) . . 286

1871 47 Speculations on the Continuity of the Fluid State of

Matter, and on Transitions between the Gaseous, the
Liquid, and the Solid States (Belfast iV. Hist. Soc.) 291

1872 48 On Relations between the Gaseous, the Liquid, and the

Solid States of Matter . . . . . . 297

1873 49 A Quantitative Investigation of certain Relations be-

tween the Gaseous, the Liquid, and the Solid

States of Water-Substance 307

1862 50 Relation between Gaseous and Liquid States [unpub-
lished Notes bearing on Andrews's Experiments] . 318

DYNAMICS AND ELASTICITY

1848 51 On the Strength of Materials, as influenced by the
existence or non-existence of certain mutual strains
among the particles composing- them . . . 334

1848 52 On the Elasticity and Strength of Spiral Springs, and

of Bars subjected to Torsion 341

1873 53 On the Principles of Estimating Safety and Danger in
Structures, in respect to their Sufficiency in

Strength 349

62

Xll CONTENTS

YEAR No. PAGE

1875 54 Comparisons of Similar Structures as to Elasticity,

Strength, and Stability 361

1876 55 On Metric Units of Force, Energy, and Power, larger

than those on the Centimetre-Gram-Second System 372

1878 56 On Dimensional Equations, and on some Verbal Ex-
pressions in Numerical Science .... 375

1884 57 On the Law of Inertia ; the Principle of Chronometry ;
and the Principle of Absolute Clinural Rest, and
of Absolute Rotation 379

1884 58 A Problem on Point-Motions for which a Reference-
Frame can so exist as to have the Motions of the
Points, relative to it, Rectilinear and Mutually
Proportional * 389

1887 59 Safety under Repeated and Varying Stresses . . 404

GEOLOGICAL

1848 60 On the Parallel Roads of Lochaber .... 407
1882 61 On Features in Glacial Markings Noticed on Sandstone

Conglomerates at Skelmorlie and Aberfoil . . 420

1877 62 On the Jointed Prismatic Structure in Basaltic Rocks . 422

MISCELLANEOUS PAPERS

1872 63 On Atmospheric Refraction of Inclined Rays, and on

the Path of a Level Ray 441

1876 64 On an Integrating Machine having a New Kinematic

Principle 452

1892 65 On certain Appearances of Beams of Light, seen as if

emanating from Candle or Lamp Flames . . 459

APPENDIX

1852 66 On Public Parks in Connexion with Large Towns, with

a suggestion for the Formation of a Park in Belfast 464

1869 67 Nationalization of Public Works 472

1867 68 Warming and Ventilating 477

INDEX . 482

BIOGRAPHICAL SKETCH

THE late Professor James Thomson, during his long and active
life, wrote numerous scientific papers which were read before the
Royal Societies of London and Edinburgh, the British Association,
the Philosophical Societies of Belfast and of Glasgow, and other
learned bodies ; but, scattered in a fragmentary manner through
the Proceedings of many different Societies, they have not hitherto
been easy of access. It has been thought desirable that the fruit
of his activity should be collected and reprinted consecutively in
a single volume.

His life is a record of long days spent in the search for
truth, and of the ample reward in new knowledge gained. The
fundamental character and value, to science and to engineering,
of the discoveries and ideas which he has given to the world, is
the feature of his work.

James Thomson and his brother William (afterwards Lord
Kelvin) are striking examples of hereditary talent ; and it would
have given their father much happiness could he have foreseen
how fully his own best qualities, as well as those of his beloved
wife, had been transmitted to their children. In fact one cannot
completely understand either of the two sons without knowing
something of their father.

Descended from a long line of farmers who had originally
migrated from Scotland to the North of Ireland early in the
17th century (about the time of the Plantation of Ulster), he
inherited those sterling Scottish qualities which have made
Ulster men so successful in turning the resources of their
province to good account. At the same time he acquired the
softer qualities characteristic of his Irish neighbours.

A letter from one of the family states that " they nearly all
bore the character of being religious, moral, patriotic, honest,
large, athletic, handsome men." They had occupied for 200 years
a farm called Annaghmore, near Ballynahinch in County Down,
14 miles from Belfast, and within sight of the noble range of

xiv BIOGRAPHICAL SKETCH

the Mourne Mountains. Here, in 1786, James Thomson, senior,
was born.

The country in the immediate neighbourhood, like that of
County Down generally, is fertile and undulating; the hillocks
are so peculiarly rounded that their appearance has been aptly
likened to a basket of eggs. Between these hillocks one finds
little valleys with glancing streams and green copses, and some-
times a clear lakelet lies open to the sky. Low-lying bogs are
few; and drainage has converted into rich meadowland many
swamps that were formerly tenanted only by the coot and snipe.
A Spa attests the fact that health-giving springs abound; and
when the South wind blows it brings with it the ozone from the
sea.

James Thomson, senior, the first of the family to leave
agriculture for scientific pursuits, was a man of remarkable
ability. When quite a young boy, having received only the
rudiments of education by the teaching of his father, he made
out for himself the art of dialling without the aid of teachers
or good books. He thus succeeded not merely in making a
sundial, but also a dial to tell the time at night by one of the
stars of the Great Bear. He used to tell his children how he
had puzzled over an old book on navigation which contained a
chapter on dialling, and felt disheartened because he could not
understand it ; and how he subsequently found that his difficulties
had arisen from the fact that the book was all wrong. One night
sitting up with his father and elder brother, Robert, to guard the
orchard, while he watched the stars slowly revolving he thought
out for himself the true principle of dialling, and made a dial for
his father's farm which told the time correctly. Robert's son, Hugh,
used to give the following account of his youthful discovery : —
" While the ploughing of a field was going on Robert and his
little brother, James, then about eleven years of age, rested at
times. The boy was then observed to be working with a slate
and a bit of stone for a pencil. In the evening after they came
home, again he began to work, having brought in a handful
of shavings from the workshop to make a blaze till the candles
should be lighted. After a little the boy exclaimed to his brother,
' Robert, I have made a discovery, I have found out how to make
dials for any latitude.' ' Can you show me ? ' said Robert, and
he showed it so clearly that his brother understood it quite well."

ANCESTRY IN ULSTER XV

Two of these rough sundials and a star dial are now in the
possession of his grandson, James Thomson.

His early progress in Mathematics was remarkable. His
father allowed him to go to Dr Edgar's school at Ballynahinch,
where he very soon made himself useful as a teacher ; and then
for four years, from 1809 till 1814, he studied at the University
of Glasgow, taking his degree of M. A. in 1812. He then attended
the classes of Theology and became a licentiate in the church of
Scotland ; and he also commenced the study of Medicine ; but on
the foundation of the Royal Belfast Academical Institution, he
was elected to the chair of Mathematics, and returned to Ireland.
He taught in Belfast from 1814 till 1832, when he was appointed
Professor of Mathematics in the University of Glasgow. He wrote
a number of important and successful school books on Arithmetic,
Geography, Trigonometry, and higher mathematical subjects.
The first of these was brought out in 1819, and new editions
have been in wide circulation up to the present day. His books
reveal originality, and constructive as well as analytical power,
qualities which we find transmitted to most of his children, but
particularly to his two eldest sons, James and William. The
gentleness, ready wit, charm of manner, and warm-heartedness
characteristic of all three, stamped them as partly Irish in spite
of the Scottish blood in their veins.

In 1816, Margaret Gardner, a young, bright and lively girl,
came from Glasgow to Belfast, to visit her relations, Dr and
Mrs Cairns, who were friends of James Thomson ; and the young
professor, then 30 years of age, was much attracted to her. She
was a daughter of William Gardner, a merchant in Glasgow,
who had fought on the British side in the American War of
Independence. His watch, which is preserved in the keeping
of one of his great-grandchildren (Agnes Gardner King), shows
the dint of a bullet which the strong case of the watch s^ved
from piercing his heart. An extract from one of Miss Gardner's
letters to her sister, Agnes, afterwards Mrs Gall, gives interesting
impressions of Belfast and the people who lived there in 1816.

" July 1816.

On Tuesday last we spent a most agreeable day at a
Dr Drennan's*. This has been our longest walk. It is more
than three miles in a most beautiful part of the country, but

* Cabin Hill, near Belmont.

XVI BIOGRAPHICAL SKETCH

indeed every way you can turn the country here is fine and always
something new ; the party was ourselves, Miss Reid, and Professor
Thomson. I never saw a more agreeable family. The Dr is a
gentleman retired upon a small fortune; he and his wife devote
their time almost entirely to the education of their family. She
has been a beautiful woman and is said to be very accomplished,
and the children from the little we saw of them seem to repay
the pains taken in their education. It is just such a place as
one would wish for, in the cottage style, white-washed and
thatched roof, but containing a good house within ; not fine,
but neat and comfortable, upon the side of a hill well sheltered
with trees; commanding to the front an extensive view of the
surrounding country, to the back the Loch with its cultivated
shores, and the Cave Hill which is a rugged mountain that forms
the termination to a range of hills on the other side of Belfast.
Belfast was hid in the valley between, but its smoke showed where
it stood. A very fine day and the season of the year gave to
these beauties their full charm ; agreeable company and good
spirits made us enjoy them. But they are far above description ;
so I leave you to fancy the Loch smooth as a lake, vessels sailing
in different directions, mountains sloping into green hills and
fertile plains, etc.

Everything about the grounds showed the 'touch of taste.'
We walked about them all the afternoon and came home by
moonlight, all agreeing we had spent a most agreeable day.
I had the honour of the Mathematician as my walking companion.
His first appearance is about as awkward as can be ; he looks as
if he were thinking of a problem and so modest he can scarcely
speak, but when tete-a-tete he improves amazingly in the way
of speaking. On our forenoon walk we had a most edifying and
feeling discussion on sea-sickness and the best mode of preventing
it. But in the evening we were much more sublime. I suppose
the moon rising in great beauty, and Jupiter shining with un-
common lustre, called forth the Professor's energies, and I got a
very instructive and amusing lecture upon astronomy."

In the following year Margaret Gardner married the " Mathe-
matician," and she became the mother of a family of seven
children*, of whom James, the subject of this sketch, was the
third child and eldest son, and William, afterwards Lord Kelvin,
the next in age.

* Elizabeth, Mrs David King, born 1818, died 1896.
Anna, Mrs William Bottomley 1820, , 1857.

James

William, Lord Kelvin

John

Margaret

Kobert

1822,
1824,
1826,
1827,
1829,

1892.
1907.
1847.
1831.
1905.

EAKLY LIFE IN GLASGOW xvii

She. was gentle and refined, pious and truthful, and with a
strong sense of humour. She directed her household with the
courage, energy, perseverance and practical commonsense so
characteristic of the Lowland Scots ; and it was a dire calamity
to her husband and to the young family, when death carried her
off a year after her youngest son, Robert, was born. All this
and much more about the influences which moulded the minds
and characters of Professor James Thomson's young family has
been gracefully told by Elizabeth King in her book on Lord
Kelvin's Early Home*.

James was born in Belfast on February 16th, 1822, and his
brother William two years later. They both developed early a
zeal for knowledge, and were encouraged in this by their father
who educated them himself with tenderest care. In fact during
these early years he was both father and mother to them, and
they never forgot it.

In October 1832, their father removed with his family to
Scotland on his appointment as Professor of Mathematics in
the University of Glasgow. Their home was in the Professors'
Court of the old College in the High Street, a fine historic group
of buildings, but situated in what had even then become a very
undesirable part of the city.

The College session lasted for six months, from the 1st of
November till the 1st of May. The long summer holidays
enabled the professors to live with their families during a con-
siderable part of each year in more healthful and congenial
surroundings. Professor Thomson used to rent a house in the
Island of Arran, at some place on the Firth of Clyde, or on the
coast of Ayrshire. There the boys had sea-bathing, learned to
swim and to row, and sailed toy boats which they made and
rigged themselves. Thus they lived a healthy, active life in
summer, spending some hours each day at lessons with their
father. James and William were, then and always, devotedly
attached to each other. From their earliest childhood they were
closely associated; all through their youthful days, in their studies
and their amusements, they were constantly together. Certain
characteristics of the two brothers were noticed even when they
were boys, which remained through life. James was the more
careful and exact, and William the more quick and ready. For

* Macmillan and Co. 1908.

xviii BIOGRAPHICAL SKETCH

instance, when making their toy boats, James was never satisfied
till his boat was finished with the utmost perfection in every
detail even to the neat painting of it; William was content as
soon as he had his boat finished enough to be able to sail, and
would not spend more time and trouble over it. In after years,
James, before publishing a scientific paper or bringing out one of
his inventions, had the whole thing long and carefully thought
over. His theories thus stood the test of investigation, and his
machine or engineering structure could be relied on to do exactly
what it was intended to do. On the other hand, his brother
William's less patient scientific work was often thrown off at white
heat, and thus subject to frequent correction and adaptation^by its
author.

At the ages of twelve and ten respectively they entered
Glasgow University together, and they very soon distinguished
themselves in every subject they took up. The younger brother,
who was even then adored by all the family as a genius, generally
took the first place and James the second. No cloud of jealousy
ever marred the friendship of the pair. The elder sympathised
with his father in the affectionate pride he took in the ability
of the younger ; and the younger was ready at all times to check
his own impetuosity by laying his ideas before the elder brother
for criticism or advice. They were unusually young, even for
those days, to be at a University ; but there was a reason for it.
Owing to a misunderstanding as to the amount of the emoluments
of his Chair, their father found himself in a very bad position
financially during the first years of his residence in Glasgow.
He could not afford to send his sons to school. Instead of this
being a misfortune, the two sons looked upon it as a very happy
circumstance for them ; and they always rated very highly their
obligations to the early grounding their father had given them.

At this time Professor James Thomson, senior, was engaged
in writing his Mathematical books; and he also found time to
conduct a class on Astronomy, to which ladies were admitted
— a novel departure at that time. This strenuous life prevented
him from taking much part in the social life of Glasgow; but
it gave his wife's relations (her cousins Mr and Mrs Walter Crum
of Thornliebank, in particular) an opportunity of showing much
kindness to the motherless family. The intimacy thus begun
with the cousins was to be cemented later by the marriage of

EARLY TRAVELS ABROAD xix

their daughter, Margaret, to William Thomson in 1852 ; while
James owed much of the encouragement he received for his early
inventions to her father's and brother's kindly interest.

In 1840 James Thomson took his degree of M.A. with honours
in Mathematics and Natural Philosophy. In the holidays of 1839
and 1840, their father had taken the young family to the Continent,
spending some time in London en route. They thus gained some
acquaintance with the French and German languages, and with
the general culture, manners and customs of foreign nations.
The diaries kept by James show the keen interest they took in
all they saw. Mechanical inventions and appliances especially
interested them.

They also much enjoyed going to the theatres with their
father's friends, and visiting museums, galleries and exhibitions.
Macready in Henry V made a lasting impression on them ; Robert
Rintoul (the son of their father's friend, Mr Rintoul, Editor of
the Spectator} took the young people to this performance. Another
friend of their father, Mr Knowles, of the same family as Sir James
Knowles, the late Editor of the Nineteenth Century Magazine, is
also mentioned in the diary.

The greater part of the first year's visit was spent by the
boys in Paris, while their father went with his two daughters
to Switzerland. The next year they all went to Germany, sailing
up the Rhine through Holland. While they were staying in Bonn
in June 1840, Professor Nichol* and his family joined them.
He took James and William for a three days' geological tour
among the hills. At Konigswinter they were joined by all the
rest of the party. The Drachenfels, and especially the sail up
the Rhine to Nonnenwerth by moonlight, made a strong im-
pression on this company of happy young people. This is how
one of them, John Nichol f, wrote about it in after years:

" ' It was upon a tranced summer night ' that we sailed round
the corner of the Rhine which reveals the Siebengebirge, and
came gliding into the island of Nonnenwerth. Clear and calm
and fair the memory of that night comes back to me from over
all the years. One by one the peaks appeared, and stood grandly
above the quiet stream, in the grey light which soon faded away

* John Pringle Nichol, Professor of Astronomy in the University of Glasgow,
1836—59.

t John Nichol, Professor of English Language and Literature at the University
of Glasgow, 1862—89.

XX BIOGRAPHICAL SKETCH

beyond their purpling crests. The moon stood out, a glorious
crescent on the ridge of Rolandseck, and a bright star led the
host of heaven over the brow of Drachenfels. The lights of the
little convent were twinkling through the trees, and the boatmen
were chanting their evensong as they came and brought us to
the shore, where we stepped hand in hand together to live what
seems to me like a dream of the gates of heaven. If my summer
on the Rhine is an oasis in my life, Nonnenwerth is the oasis
within the oasis, the greenest and most beautiful spot amid the
whole of this enchanted ground*."

More than sixty years later, when Lord Kelvin came to visit
his nephew in Newcastle-on-Tyne, and his father's diary of this
little tour was shown to him, this was the incident that taught
his attention ; and he enlarged upon it in such a way that those
who listened felt that he loved to dwell on it.

Shortly after this, James unfortunately injured his health
when walking with his brothers William and John in the Black
Forest. He hurt his knee in some way, but did not complain at
the time. He had already decided to adopt Civil Engineering
as his profession, and, after his return from Germany, he entered
Mr (afterwards Sir John) McNeil's office in Dublin, but in three
weeks ill health obliged him to give up work and he returned
home quite lame. He had a good friend in John K McClean, who
afterwards attained a great position in the early days of railway
construction. They had been fellow students in his father's class,
and McClean had been one of the Professor's favourite pupils.

A characteristic letter of McClean's refers to one of James's
earliest inventions, a boat which, by means of paddles actuating
jointed legs reaching to the bottom, is able to propel itself up
a river — walking against the stream.

"WALSALL, 15th Nov. 1841.
MY DEAR JAMES,

I was much gratified at receiving your note of the
6th Inst. and if it had been longer would have relished it still
more. Whenever you have leisure I will feel obliged by your
writing me a few lines. I regretted much not seeing your father
when he was in England and also your postponing your visit, but
I will hope to see you in Spring for some months when we may
be mutually serviceable. I am glad to find that you will be able
to attend the Civil Engineering Class this session — no doubt you

* See Memoir of John Nichol, p. 26 (MacLehose and Sons).

EARLY ENGINEERING EXPERIENCE XXI

will derive much benefit from it. If Mr Gordon* has published
the heads he proposes lecturing on, I will be much obliged by
your sending me a copy by post.

Your scheme for propelling vessels against the stream is very
ingenious. Altho' you have not been aware of it and have equal
merit as an inventor, it was tried in France many years ago.
If you refer to a Book entitled Machines approuvees par I'Academie
des Sciences you will find four schemes proposed.

I have given you these in detail that you may be able to
judge whether your scheme is similar. If so, as I said before,
I do not consider that it lessens your merit as a discoverer in
the slightest degree. There is one thing it may however prove,
the great difficulty of hitting upon any useful scheme that has
not been previously attempted, and the necessity of examining
well before one expends time on such occupations.

Indeed were I you, and I am sure you will excuse me as a
senior apprentice, I would, for the present, avoid all attempts at
inventing machinery of any description.

After a few years have gone round and you have become
well acquainted with the principles of mechanism and with the
discoveries and failures of others, you will be able to bring a
mind well stored to the task, and from knowing the wants of
practical Science be able also to fill them up.

It seems to me to be nearly as great a waste of time, making
attempts at useful discovery without this previous knowledge, as
for a person to labour at working out the highest problems in
Astronomy without having first gone through the Calculus.

I cannot avoid speaking feelingly, my dear James, upon this
subject, as I lost a great deal of time and spent money on making
a rotatory steam engine, which, when finished, I found had been
patented ten years before.

Believe me my dear James Yours sincerely

J. R. McCLEAN."

In 1842, having considerably improved in health, Thomson
went for some time to Walsall (not as a pupil nor as an employe,
but simply as a friend) to learn what he could by practical experi-
ence under Mr McClean's guidance.

Early in 1843 he went to the Horsely Iron Works, Tip ton,
Staffordshire, where he remained for a few months as a pupil in

* The first Chair of Engineering in the United Kingdom, probably the first in
the world, was that founded by Queen Victoria in 1840 in the University of Glasgow.
Lewis D. B. Gordon held it from 1840 to 1855, and James Thomson was a student
in his class of 1841—2.

XX11 BIOGRAPHICAL SKETCH

the drawing office. In August, to his great satisfaction, he was
apprenticed to Mr (afterwards Sir William) Fairbairn, his father
paying £100 as his apprenticeship fee, and he began working in
Fairbairn's Engine Works at Millwall, London. Messrs Wm.
Fairbairn & Co. were well known as the first millwrights and
among the first engine makers in Britain.

McClean in writing to congratulate him says " I have always
considered your health as the only obstacle to your being "a first
rate practical engineer. I feel confident that you have the talent
for it."

Unfortunately his health was not equal to the strain of working
in the damp unhealthy surroundings at Millwall. He suffered
from continual colds as shown by the following extracts from his
letters to his father.

"MILLWALL, Oct. 8, 1843.

The Isle of Dogs I find is a very unhealthy place ; and the
workmen are often obliged to leave it soon after they come, on
that account. The ground is low and marshy, and a kind of rank
smelling fog rises for several feet from it in the evenings. I have
had a cold now for some weeks, and have been coughing a little in
the mornings, but not nearly so much as when I went down to
Southannan*; and I think that when I get to my new lodgings,
by wearing plenty of clothes and staying in the house almost
entirely after work hours I shall be able to get on quite well."

"MILLWALL, Oct. 10, 1843.

Since last Friday I have been taking holidays from the works
on account of my cold, and taking quick walks (half walking and
half running) with a great deal of muffling. In this way my cold
is now beginning to get better, and I think that in a few days
more I shall be able to go back to the works. In the house I am
reading the Hot Blast Trial, which is I think the most useful
book I could have on Engineering.

I am very glad to hear that the Algebra has been getting on
so well. You must let the Trigonometry wait for a while, as it
would keep you too busy when the Session begins. One of the
workmen with whom I have had some conversation, as he worked
beside me for some time, asked me to recommend him some simple
book on mensuration ; so I lent him your Arithmetic on account
of the article in it on mensuration. He has been greatly taken
with it, and has been sometimes sitting up late at night and

* Southannan was an interesting old house on the Clyde which Dr Thomson
had rented for summer quarters that year.

EARLY ENGINEERING EXPERIENCE xxiii

sometimes rising at 4 or 5 in the morning to read about fractions,
common multiple, proportion, square root, cube root, &c. and to do
the examples and exercises."

"MILLWALL, Nov. 24, 1843.

I cannot say that it [my cold] is getting better yet, although I
have now been away from the works a fortnight and four days, and
have been taking all the care I could."

While he was working at Millwall he was interested in a
method for preventing smoke in furnaces, which he had thought
of. The gases were to be taken downwards through the furnace
instead of upwards ; and the fire-bars were to be tubes with water
circulating through them.

In October 1844 James Thomson was transferred to Messrs
Fairbairn's Manchester Works, a welcome change, seeing that
it afforded more opportunities for personal intercourse with
Mr William Fairbairn who lived -there. He moved into lodgings
from which he wrote to his father " One might as well live in a
chimney as live near the Works." He remained in the fitting
shop until ill-health interrupted his progress in his profession.
There was some derangement of the heart's action ; his pulse beat
too quickly — as much as 120 a minute — and he felt weak and ill.
He wrote to his father, "I confess I feel very uneasy about it.
I wonder if there is any likelihood of my getting stronger as long
as it [the pulse] continues to go so fast as it has been lately or if
it is likely to begin to go slower."

At the end of the year he returned home to Glasgow; his
medical adviser there, a stern old Calvinist, told him he had heart-
disease and might 'die at any moment, and advised him to put
away from his mind all thoughts of this life and prepare himself
for the other world. Happily this diagnosis turned out to be
wrong. The distressing symptoms were the result of temporary
disturbance. After some years he completely recovered his health,
and was able during the remainder of his long life to enjoy active
exertion both of mind and body. But at the time the verdict
seemed a death sentence, and the effect on a man of twenty-three,
at the very commencement of his career, might easily have been
to render him a complete invalid. Happily his natural energy
saved him from this, and when bodily exertion was prohibited, he
turned his mind with undiminished activity to such pursuits as
remained possible. His correspondence and note books show the

XXIV BIOGRAPHICAL SKETCH

varied interests with which he occupied his mind. The following
letter to Mr Robert Murray, one of Messrs Fairbairn's staff at
Mill wall, on the subject of obtaining fresh water from salt by
double distillation, is interesting from its very modern attitude to
the problems of economy of power, and from the partial anticipation
of subsequent ideas on available energy, regenerative action, etc.,
which is tacitly involved in it.

"October, 1845.

I received your two letters regarding the apparatus for
distilling sea water, and I am much obliged to you for the full
account you have given me of it. Two methods had occurred to
me, different from one another, but yet involving the same principle
of making the heat which is given out in the condensation of the
steam serve to generate new steam. The one is exactly the same
as you describe, and in it you will see that the fresh water is
separated from the salt by the expenditure of a certain quantity
of heat. In the other method, which so far as I could judge
appeared to be the preferable one, the effect is produced by the
expenditure of labour. The steam is generated in one vessel
(in the first instance by the heat of a fire) and it is pumped from
that into another which is placed within the first. The pressure
applied to the steam by the pump raises its sensible temperature
slightly, and therefore allows the heat to pass back through the
metal to the first vessel, there to generate exactly the same
quantity of steam as is condensed in the second. Hence if the
salt water be supplied at the boiling temperature, no supply of
heat will be required to produce the chemical effect of separating
the fresh water, but only a very small quantity to make up for
the cooling of the apparatus by the external air. But it is easy
to arrange the apparatus so that the salt water entering the steam
generator will be raised almost to the boiling point by the heat
contained in the condensed water and in the brine.

In relation to the quantity of fresh water which could be
produced by the labour of one man applied to a machine of
moderate size, I have made such calculations as convince me that
the plan is not at all impracticable. The only data however to
found the calculations on which I have as yet been able to obtain,
are too vague to enable me to come to any decided opinion as to
whether this or the first plan would be preferable.

The apparatus for the second would no doubt be more ex-
pensive than that for the first plan, but the supply of coals
required for the second would be but a very small fraction of that
required for the first. The labour of the sailors I suppose is not
of very much consequence, as they have but little to do except in
stormy weather, and when going into and out of ports.

We have now come up to Glasgow from our summer quarters.

EARLY THERMODYNAMIC IDEAS XXV

I don't know whether you are acquainted with Glasgow, but if
you are, you will know that the College is in a very bad part of
the town.

On this account I am very glad to say that the College grounds
are wanted for a general terminus for a number of railways, for
which purpose they are admirably suited. There is a great
probability that the matter will be arranged to the- satisfaction
of the different parties concerned, and that the College will be
moved to an excellent situation in the West end of the town*."

The plans expounded in this letter for the recovery of waste
heat, by raising it to a higher temperature by the expenditure of
mechanical work, show how his thoughts were ripening in the
direction of his forthcoming thermodynarnic discoveries.

The spirit in which he studied Nature is indicated by extracts
written on the title-page of his note-book on Natural History,
dated March, 1846.

My heart is awed within me, when I think

Of the great miracle which still goes on,

In silence, round me — the perpetual work

Of Thy Creation, finished, yet renewed

For ever. [Forest Hymn, BRYANT.]

Thou art, 0 God! the life and light

Of all the wondrous world we see ;

Its glow by day, its smile by night,

Are but reflections caught from Thee. [MooRE.]

In the note-book itself we find squares very neatly marked out
with an alphabetical index for different subjects: for example,
" Temperature and Pressure of Atmosphere " under A ; " Design
in Creation " under D ; " Expansion of Ice " under I ; " Glacial
Period and Glacial Markings in Glen Spean," G ; " Lakes, how
formed," L ; and " Parallel Roads " under P. The illustrations,
pen and ink sketches, of Rock Strata and River Basins are excellent
in execution ; and so are the sketches of molluscs in the notes on
the Classification of Fishes by Agassiz.

Broadly speaking, his most important discoveries may be said
to follow in sequence along three main channels or streams of
thought ; and we can trace each one back to its rise in these years
when the note-book was in progress and the waterwheel being
worked out.

* "This proposal fell through for a time, but some 20 years later the old College
was bought by one of the Railway Companies and the present University building
erected on Gilmorehill."

T. G

XXVI BIOGRAPHICAL SKETCH

His study of the laws of fluid motion led to his discovery of the
Whirlpool of Free Mobility, to his Patent Vortex Turbine, and to
his Jet Pump. Later on, his professional work in designing turbines,
and his duties as engineer to the Belfast Water Commissioners, led
him to study the measurement of water in rivers and streams,
which resulted in the introduction of the V-notch gauge. Similar
considerations led on to a series of important investigations into
various aspects of the motion of water in rivers.

At the end of his life he returned to a subject which had first
attracted him when he wrote a paragraph on Trade Winds for
a new edition of his father's Geography, brought out in 1846,
namely that of the general Atmospheric Circulation. Finding no
satisfactory explanation of this problem he formulated his own
theory and developed it at various periods of his life (see papers
Nos. 26, 27, pp. 144, 148). He summed up all his ideas and gave
a very complete and detailed explanation of his theory in his
Bakerian lecture finished just two months before his death and
read at the Royal Society by Lord Kelvin in March, 1892 (see
No. 28, p. 153).

The second train of thought, that of Thermodynamics, led him
on from the " Lowering of the Freezing Point by Pressure," a
discovery first published in 1849, to the principles underlying the
Plasticity of Ice ; and finally to the papers on the transitions
between the Gaseous, Liquid and Solid States of Matter.

The third group, starting with papers on Elasticity, passes on
to the Strength of Materials and the Safety of Structures.

Another important series of papers relates to the question of
absolute and relative motion, which has recently assumed fresh
prominence in the philosophy of physical science. It is interesting
to find that in the paper on the Law of Inertia in 1884 (p. 379),
he has developed an idea sketched out in a letter to his brother as
early as May 7th, 1848.

"Did you ever observe that we might a priori have just the
same difficulty in fixing on equal additions of time at different
periods as we have in fixing on equal changes of temperature at
different temperatures ? There is nothing in the human mind to
determine what time three months hence shall be equal to a certain
time to-day. What one man thinks a long time seems short to
another. We might adopt the time from the Sun's coming to the
meridian till his reaching it the next day as a unit of time. Then
it would be the case that a body not subjected to force would not

SCIENTIFIC WORK xxvii

move over equal spaces in equal times, &c., &c. There would thus
be many very complicated and puzzling laws of motion, which
would at once be all simplified when any one said, Let us change
the scale of time, and take as equal times those occupied in
describing equal spaces, or those in which equal velocities are
generated by a constant force."

The various methods of utilizing the natural sources of power
in our rivers and waterfalls had always a strong fascination for
him. His early diary shows that he took particular notice of the
waterwheels in Holland. He would naturally be introduced to
the French turbine by Professor Lewis Gordon in his classes at
Glasgow. With thoughts thus running on these lines, he gradually
developed his Vortex turbine, which afterwards became so successful.
Extracts from two letters to John McClean show the progress of this
invention.

"Christmas Day, 1846.

Since our return from the country in the end of October,
I have been making a model of a horizontal waterwheel, on what
I consider to be an improved plan. The idea of this occurred to
me long ago, in fact, before my visit to you at Walsall ; but,
following your advice, I laid it on the shelf along with some others,
trusting that any good ones among them would keep, and that the
useless ones would moulder away without occupying time which
ought to be devoted to more regular business. Now, however, after
having been so long nearly inactive, I enjoy this light occupation
very much ; and even if the thing should in the end not turn out
to be of any pecuniary advantage to me I shall not consider the
time to have been thrown away."

"April 12, 1847.

About the beginning of the year I mentioned to you that
I had made a small model of a new waterwheel. I have since
been staying for some time in the country with a friend of ours,
Mr Walter Crum of Thornliebank and at his works, which are very
extensive and varied in their character, a large model of one of my
wheels was constructed and its performance carefully tested by the
friction dynamometer of Prony (frein dynamometrique, as you may
have seen it called by French authors). The model worked to a
tenth of a horse-power, and produced between 69 and 70 per cent,
of the total work due to the water expended. As the best overshot
waterwheels are only estimated to produce 75 per cent., and as
there are some defects in the workmanship of the model, the
result was very satisfactory. I should have mentioned that mine
resembles the French turbine, and Whitelaw and Stirrat's wheel,
in being of very diminutive size and of small cost in proportion to

c2

XXV111 BIOGRAPHICAL SKETCH

its power ; and I consider that besides prod ucing more work than
they with a given quantity of water, it will be free from some
important practical objections which apply to them. I have
matured two other forms of wheels depending on the same general
principles as those I have already constructed but which I believe
will be considerably superior in efficiency and I am just com-
mencing to get large models of them made in Glasgow."

When his invention was completed the question of a patent
was carefully gone into by his father and friends, an important
factor in the consideration being the fear that his delicate health
would prevent his working the invention effectively. Finally the
patent was taken in July, 1850, and various engineers were
licensed to manufacture the turbine for him. The principal
manufacturers were Messrs Williamson Bros., of Kendal.

The following letters show how ready William Thomson was
to help his brother with his patent work ; while the reference to
Joule's early papers gives them a very special interest in the early
history of Thermodynamics *.

"ST PETER'S COLLEGE.

July 12 (12h 30a.m.), 1847.

MY DEAR JAMES,

I am going from Cambridge to-morrow afternoon (or
more properly to-day) to London, where I shall remain as few days
as possible, before starting for Paris. I enclose Joule's papers
which will astonish you. I have only had time to glance through
them as yet. I think at present that some great flaws must be
found. Look especially to the rarefaction and condensation of air,
where something is decidedly neglected, in estimating the total
change effected, in some of the cases. Keep all the papers
carefully together and give them to me when I return. I am
glad your patent is getting on. Tell me immediately what you
want me to do in Paris, writing to the Paste Restante. I shall
arrive there about Saturday

Your affcte brother,

WILLIAM THOMSON."

"PARIS, July 22, 1847.

MY DEAR JAMES,

I was introduced to Poncelet (having accidentally

met him at a party to which Le Verrier took me) and I had a
great deal of conversation with him. I was quite taken with him,
as he seems to be a most excellent old man. I mentioned your

* Cf. " Obituary Notice of Lord Kelvin," by J. Larmor, in the Proceedings of the
Eoyal Society, Series A, Vol. LXXXI. June 30, 1908, pp. xxv. xxix.— xxxvii.

TURBINES AND WATER-WHEELS xxix

wheel and asked him about patents etc. He told me, before
I described yours at all, that he has invented a 'Turbine a
injection exterieure ' and that although he has not published any
account of it, yet there are several of them working, in the South
of France. He made an appointment for me to call on him at his
own house, so that he might explain it to me. When I went
there he showed me some sketches and explained it a little, but
still I am not quite sure that I understand it. There are passages
in the wheel, curved I suppose on the same
principle as the common turbine. The sides
of the passages are 'enfonte,' and are double,
leaving a vacant hollow space (the black-
ened parts) which he considers useful in
modifying the form of the aperture.

The water is introduced by a number
of, apparently tangential, passages, and the
centrifugal force is overcome by fluid pres-
sure. The wheel is I think about half
under the level of the reservoir, into which
the water is discharged (I suppose down-
wards) from the centre of the wheel. If you think yours is very
like his, the title of the patent should (as he told me) be "brevet
de perfectionnement pour la turbine a injection exterieure de M.
Poncelet."

I do not know however whether any of your modifications
(unless the 1st. kind, with curved passages) could be viewed in
the light of an improvement of Poncelet's. With reference to the
advantages of Poncelet's over ordinary turbines, one which he laid
some stress on is that, when the supply of water is very slight the
wheel works to best advantage, the reverse being the case for
turbines. He gave me the following particulars (dictated partly,
and partly he wrote in my pocket book) relative to one which has
been constructed "Turbine a injection exterieure etablie a Toulouse
par M. Abadie, ingr.

Shute 1*7 met. depense maxm. 650 kil. d'eau
650 k. x 1-70 rn. = 1105 kil. met.

14*73 chevaux dynam. rend an maxm. pour le faible depeuse
de 140 k. (per minute, I suppose) 0'68 (of the power) pour les
grandes de 170 kil. (there is some mistake of course) rend seule-
ment 0'50."

With the expenditure 160, intermediate between the two
former " 0'60 du travail absolu." The velocities of the wheel in
the three cases were 41, 43, 41 turns per minute respectively.

Exterior diamr. 1 m. 20. Inter. 0'80.

Poncelet considers his turbine better than Fourneyron's (which
is now falling out of use, or at least of being made) I believe in

XXX BIOGRAPHICAL SKETCH

every case in which a horizontal wheel ought to be employed,
sometimes it would be advantageous, sometimes an overshot
wheel, and sometimes a breast wheel (he has been making
improvements in the last mentioned "Les Brist-weeles ne vont
pas assez vite ") according to the fall or the kind of work wanted.
For cotton mills he agreed with me that turbines would probably
be preferable. About the end of this year he will have a memoir
on waterwheels published.

Since Monday I have been as busy as possible (before that
I could find nobody and get nothing done), commencing by calling
on Le Verrier to whom I had been introduced at Cambridge by
Mrs Hopkins. He engaged me to go to Mr Milne Edwards in the
evening, with whom he and Struve were going to dine.

I breakfasted with him next morning and he took^me and
Struve and a little son of his own to Versailles, where we were
for the day; but before I breakfasted with him I saw part of the
Cabinet de Physique of the Polytechnic, to which he got me
admitted, made engagements with Regnault the preparateur at
the Polytechnic &c. I have been all day to-day and a good part
of yesterday at Marloye's shop, where I ordered a great quantity
of acoustical apparatus. Mme. Dubuat is away for 2 months.
I start for Geneva to-morrow at 10.30.

W. T."

"EOENBARNET BY DUNTOCHER.

July 24, 1847.

MY DEAR WILLIAM,

Three papers have come for the Journal* from

Newman f . None of them is very long but they would cost several

shillings if they were sent to you. The first is regarding Fourier's

/»«
theorem: the second regarding \ e~xaft-ldsc. The last is a de-

J o
velopment of (cos#)a.

I suppose you got two letters at the Poste Restante in Paris
from me ; and I hope you have been able to do something with
the one I enclosed to you from Mr MacGregor. I wrote yesterday
to Mr Fairbairn on the subject of my wheels, just asking generally
whether he could give me any useful information as to the way in
which I ought to proceed.

I have read a good deal of Joule's papers and I certainly think
he has fallen into blunders. There is one blunder certainly. He
encloses some compressed air in one vessel, connects that with
another which is vacuous, and allows the air of the former to rush

* [The Cambridge Mathematical Journal, then edited by W. Thomson.]
t [The late Professor F. W. Newman, brother of the Cardinal.]

EARLY CORRESPONDENCE WITH LORD KELVIN xxxi

into the latter till the pressure is the same in both. Both vessels
were immersed in water, and after the operation the temperature
of the water remains the same as before. Joule says that no
mechanical effect has been developed outside of the vessels during
the operation, and that therefore the heat remains unchanged.
But in reality mechanical effect was developed outside*, as the
two vessels became of different temperatures. Some of his views
have a slight tendency to unsettle one's mind as to the accuracy
of Clapeyron's principles. If some of the heat can absolutely be
turned into mechanical effect, Clapeyron may be wrong. I think,
however, that before coming to a conclusion, we would need to
define more accurately what we mean by a certain quantity of heat
as applied to two bodies at different temperatures. Perhaps
Joule would say that if a hot pound of water lose a degree of
heat to a cold one, the cold one may receive a greater absolute
amount of heat than that lost by the hot one ; the increase being-
due to the mechanical effect which might have been produced
during the fall of the heat from the high temperature to the
low one.

I am your very affectionate brother,

JAMES THOMSON."

"EDENBARNET, BY DUNTOCHER, DUMBARTONSHIRE.
July 29, 1847.

MY DEAR WILLIAM,

I got your letter to-day and I am glad to find that
you have seen the gentlemen to whom I sent you introductions.
The only thing in regard to Poncelet's wheel which gave me any
uneasiness was the expression you used that ' The water is intro-
duced by a number of apparently tangential passages and the
centrifugal force is overcome by fluid pressure.' Now are you
sure the cent, force is overcome by fluid pressure transmitted
directly from the stationary part of the apparatus ? In other
words, does the water in passing through the orifices of the
tangential passages attain the velocity due to the whole fall ; or
only to half the fall as in mine ? From the form of the vanes you
drew, as well as from its being thought desirable to make the
vanes double with an empty space between the two parts, I think
that the water must attain the velocity due to the whole fall, or
nearly so, as is the case in Poncelet's wheel of which I have seen
published accounts. I have often thought myself, that in that
wheel, and in the turbine of Fourneyron, it would be advantageous

* [Joule meant of course mechanical work. This passage illustrates the early
difficulty in distinguishing the varying mechanical availability of heat from the
steady conservation of its amount.]

XXX11

BIOGRAPHICAL SKETCH

to have the vanes made double, but in mine there would not be
the least use in such a construction.

Poncelet's as drawn by you.

My Wheel.

In mine you will see the outer ends of the vanes are in the
direction of radii or nearly so ; but in Poncelet's they are nearly
tangential. This tangential direction makes me think he intends
that the water should spout in with a much greater velocity than
that of the wheel, in which case it will be impelled towards the
centre by its own impetus as it glides along the curved buckets.
The action of mine would not be materially altered by even a
considerable deviation of the outer ends of the vanes from the
direction of the radii : but when the direction comes to be nearly
tangential the action is entirely altered, and I think it assumes
the character of that of Poncelet's. When the ends are nearly
tangential the space between the vanes
at the outside is greatly contracted. Then
this renders it desirable to make the
vanes double, so that the width of each
passage for the water may not be greatly
increased towards the middle. In mine
the water has no rapid motion in relation
to the wheel at the parts near the cir-
cumference, and hence a moderate altera-
tion in the form of the buckets would be
of no consequence : but I believe this is
not the case in Poncelet's. In Poncelet's
old wheel the water was admitted by only
one orifice, and the circumference of the
case was not spiral but circular and concentric with the wheel.
Hence the water acted on only one side of the wheel, the rest of
the wheel being filled with air, and some of the buckets being
partly filled with air and partly with water. His new wheel, which
you say has several tangential passages for bringing on the water,
must be better and more like mine. I think, however, from what
I have said it will appear to you to be different in principle from
mine; and if the water in his be discharged only below, mine
must have a great practical advantage in discharging both above

Poncelet's Wheel, of which
I have already seen ac-
counts.

TURBINES AND WATER-WHEELS xxxiii

and below. Did Poncelet say anything to you regarding the way
in which he regulates the size of the orifices so as to make them
suitable for different quantities of water? I have a very good
regulator for mine

I am, Your affte. brother,

JAMES THOMSON/'

Many turbines were made under James Thomson's patent, and
were erected in various parts of England, Scotland, and Ireland,
while some were sent abroad. They were very successful, and at
the International Exhibition of 1862 a medal was awarded for
" originality of design, practical success, and good work." The
Encyclopaedia Britannica* says:

" Professor James Thomson's inward flow or vortex turbine has
been selected as the type of reaction turbines. It is one of the
best even in normal conditions of working, and the mode of
regulation introduced is decidedly superior to that in most reaction
turbines ; it might almost be said to be the only mode of regulation
which satisfies the conditions of efficient working, and it has been
adopted in a modified form in the Leffel turbine, which is now
largely used in America."

At an early age he became deeply interested in questions
dealing with glacier motion. Writing on 13th February 1847 to
his sister Anna (Mrs Wm. Bottomley), he says, " On the Friday
before last Professor Forbes came here [Glasgow College] on a visit
to us, by William's invitation....! had a good deal of conversation
with him ; especially in regard to glaciers and their bearing on
the Parallel Roads of Lochaber, about which perhaps Robert has
told you I have been writing." On April 5th of the same year
there appears a memorandum in his handwriting : " This morning
I found the explanation of the slow motion of semi-fluid masses
such as glaciers."

He had read all that had been published on the Parallel Roads
of Lochaber though he had never been in the district himself; but,
studying the subject from books and maps, he supplied the missing
link in the chain of reasoning that was necessary to substantiate
the explanation begun by Agassiz. He showed that certain loca-
tions of glacier barriers which were perfectly possible would explain
the positions of all these terraces. His paper (No. 60, p. 407), read

* Ency. Brit. 9th Edition, Vol. xii. 1881, page 527, article "Hydro-mechanics,"
by Sir A. G. Greenhill, F.B.S., and Prof. W. Cawthorne Unwin, F.B.S.

XXXIV BIOGRAPHICAL SKETCH

before the Royal Society of Edinburgh on March 6th, 1848, enforces
that view, now the accepted explanation. On the same night, the
Secretary, Dr William Gregory, wrote a long letter to the young
author, telling him of the enthusiastic reception of this, his first
paper, and inviting him to send others. Thus encouraged, he
turned his mind more and more to pure science rather than to
practical engineering. His next two papers appeared in the
Cambridge and Dublin Mathematical Journal of November 1848,
in which year his brother took over the editorship of that
journal. The first (No. 51, p. 334), " On the Strength of Materials
as influenced by the existence or non-existence of certain mutual
strains among the particles composing 'them " is reproduced in
extenso (with a few changes made in it with the author's con-
currence) in the article on " Elasticity " written by Sir William
Thomson for the Encyclopaedia Britannica, 9th edition, Vol. vn.,
p. 798. The second was " On the Elasticity and Strength of
Spiral Springs and of Bars subjected to Torsion."

On January 2nd, 1849, he communicated to the Royal Society
of Edinburgh his famous paper on the " Lowering of the Freezing
Point of Water by Pressure " (No. 29, p. 196), which showed how
thermodynamics, by passing beyond the mere discussion of heat
engines, could become the ground subject of the physical sciences.
In this paper he not only showed by the application of thermo-
dynamic principles, that the freezing point of water is not a fixed
temperature ; but by calculations founded on the known values of
the latent heat of fusion of ice and the pressure of aqueous vapour
near the freezing point, and the known expansion of water in
freezing, he predicted, in advance of all experiment, the exact
amount of the lowering of the freezing point of water which
would be produced by the application of a given amount of
additional pressure.

The importance of this new development was at once grasped
by his brother, William, who soon confirmed it by accurate experi-
ments. The classical papers dealing with this matter have already
been reprinted many times, for example in Sir William Thomson's
Mathematical and Physical Papers, Vol. I. pp. 156, 165. But
James Thomson's paper, as reprinted in Phil. Mag. in November
1850, has another title to interest, which is not so generally known.
In it, by means of an alteration of one sentence *, for the first time
* See infra, p. 201 footnote.

PROPERTIES OF ICE XXXV

Carnot's principle was stated, and Carnot's cycle described, in
words carefully chosen so as not to involve the assumption of the
material nature of heat, or rather as Thomson himself puts it, the
supposition of the perfect conservation of heat.

The principle of liquefaction by pressure, thus established, was
afterwards (in 1857) used as the foundation of his well-known
explanation of the Plasticity of Ice*, a phenomenon which had
been impressed upon Forbes by his observations on the motion
of glaciers. Later, from 1857 onwards, for several years the
whole subject afforded James Thomson much food for thought;
extensions and developments followed on the. influences of physical
environment on crystallisation and on other changes of state.
These pregnant indications of general laws obtained due recog-
nition, when the subject assumed in 1876 its ultimate quantitative
form in the profound work of Willard Gibbs.

Many questions of secondary importance but of considerable
interest, arising from the foregoing investigations, occupied much
of his time and attention. A paper read before the Belfast
Natural History and Philosophical Society on the 7th May 1862
(No. 40, p. 258), on Ground or Anchor Ice, offered an explanation
of the phenomenon which is so great an impediment to the
navigation of the St Lawrence at Montreal, and which has been
recently minutely examined by Professor H. T. Barnes and other
Canadian physicists under the auspices of the Canadian Govern-
ment with a view to the discovery of a remedy. The actions
which accompany the solidification of crystalline substances out of
liquid solutions are used to explain the atmospheric disintegration
of stones in a paper read before the British Association in 1862
(No. 39, p. 257). On the 20th April 1864 he brought the same
subject before the Belfast Natural History and Philosophical
Society, and, at the same time, he made a communication on
the "Tubular Pores in Ice Frozen on Still Water"; two years
previously he had given in a letter to his brother, printed infra
(No. 33, p. 220), the substance of this explanation. On the same
evening he made some remarks on " Conditions affording Freedom
for Solidification to Liquids which tend to Solidification, but
Experience a Difficulty of making a Beginning of their Change

* "On the Plasticity of Ice as manifested in Glaciers," Proc. Royal Society
1st April 1857 (No. 31, p. 208) and "On the Plasticity of Ice," Brit. Assoc. 1857
(p. 211).

XXXVI BIOGRAPHICAL SKETCH

of State"; he spoke apparently without notes, but a manuscript
in his own hand written on the following day has been printed
here (No. 41, p. 268).

A paper probably to the same effect as the paper of 1862
on " Disintegration of Stones " was read before the Philosophical
Society of Glasgow on the llth April 1877, " On some of the
Chief Modes of Decay of Stones in Buildings." There is no
copy preserved.

In the early months of 1864 he made a minute study of a
familiar phenomenon, the pushing up of the level of the ground
in times of frost. A sketch — reproduced below, p. 269 — explains
what he observed of the action of the frost in producing separating
spicules of ice in the soil ; he made it the subject of a paper to
the British Association in 1871 (No. 42, p. 270).

Besides the main lines of thought there are a number of
miscellaneous papers. No one who reads these works can fail
to be struck by the fact that the author possessed in a higher
degree than most men the gift of penetrating to the heart of
his subject, and so to say of feeling the cause of the natural
phenomena he observed. He had the faculty of nursing theories
in his mind, and working them out in every detail. Instances
of this completeness will be found in the papers on the " Lowering
of the Freezing Point by Pressure " ; " On the Flow of Water
in River Bends"; "On the Parallel Roads of Lochaber"; on
" Columnar Structure " ; and " On Atmospheric Circulation."

Another characteristic trait, to quote the words of his favourite
pupil Dr Archibald Barr, " was his endeavour at all times to reach
the greatest possible clearness in his own thoughts, and his
scrupulous conscientiousness in endeavouring to impart to others
in the clearest and least ambiguous language attainable the exact
ideas he desired to convey." This led him to be unusually careful
in his choice of language, and as a result of this trait in his
character he often could not find a word that exactly suited his
purpose. Thus many new words were introduced, some of which
are now well established in scientific language.

This trait made him very chary of expressing an opinion until
he felt quite sure of it. He thus produced a smaller amount of
scientific work than might have been expected from his constant
occupation with it. The same mental attitude debarred him from
teaching his classes any new or hypothetical doctrines until he

PHILOSOPHIC VIEWS XXXvii

had satisfied himself that they were sound. To one who was
starting for Japan in order to assume professorial duties he gave
the advice, " Teach only what you know to be true."

It is therefore all the more interesting to find a man of so
conscientious and straightforward scientific mind insisting again
and again on his firm belief in Design in Creation and in the ever
acting power of the Creator. In discussing The Vestiges of Creation,
which had then been just recently published anonymously*, in a
letter to his friend Robert Douglas, he writes :

"Aug. 15, 1846.

I do not like the development theory as given in The Vestiges.
It appears to me that the author substitutes for the Creator, what
he calls Law; and that, if he gives his assent to the existence
of God as a First Cause, he, at least supposes Him to be now
infinitely removed from all the Works of Nature, and that every-
thing goes on now of itself just as a clock goes after its weights
have been wound up. Now I am strongly impressed with the
idea that a law is in itself nothing and has no power ; and I can
view what we call the Laws of Nature in no other light than
merely as expressions of the will of an Omnipresent and Ever
Acting Creator."

At the end of this year, 1846, his brother William was
appointed to the Chair of Natural Philosophy at the University
of Glasgow, and James, who was then still living at home, attended
his classes in 1847 — 8. At this time he assisted his father by
drawing an astronomical plate for the Atlas to accompany a new
edition of the Geography. That winter Professor James Thomson
and his son William both sat for their portraits to Graham Gilbert.
Writing to William Bottomley on 25th December 1847 James
Thomson mentions these portraits. " My father, Mrs Gall, Robert
and I drove to-day to Graham Gilbert's and saw the portraits of
my father and William — I think them both very good."

When at Blairlogie in 1848 a medical adviser who had been
called in to see his sister Mrs King was asked to examine him
also, with the result that a much more hopeful view was taken
of his condition ; the lowering diet prescribed by the doctor who
had previously told him he had heart complaint was to be entirely
given up. With a more natural mode of life a more natural heart
action was set up ; gradually strength returned, and in a few years,

* The author as is well known turned out to be Kobert Chambers, the publisher,
of Edinburgh.

XXXV111 BIOGRAPHICAL SKETCH

to his great joy, he found he could again take up engineering as
a profession, in spite of all the dismal prognostications to the
contrary.

It may be interesting at this point to have a side-light thrown
on his personality, taken from the Memoir of John Nichol*, his
friend and in after years his colleague at the University of
Glasgow. Talking of the Thomson family Nichol thus describes
the eldest son. " Of the sons I liked James best. He was
crotchety and apt to be sulky with those who would not enter
into his crotchets; here, as far as I know, his faults end. He
was steadfast, independent, straightforward, quiet, unobtrusive,
with more Scotch than Irish blood in his veins, and yet * it ran
warmly enough for his friends, and at a later period I had the
honour to be one of them. His passion was engineering; he
was always on the eve of inventing something that was going
to revolutionize trade. He used to show me lots of models, and
often when we were in Arran together he would walk out to
try his boats or his wheels on the streams, as a chemist goes to
make an experiment that will test the worth or worthlessness
of years of toil, or the astronomer goes to look for the star
whose place he has predicted with the help of a million figures.
I believe some of these inventions were excellent, but there was
always some practical obstacle which prevented their bringing
to the inventor either the fame or the fortune they merited.
James was an idealist in his way...."

In the winter of 1848 — 9 an epidemic of cholera devastated
Glasgow, and carried off many of her most valued citizens,
among others Professor James Thomson senior, who died on
January 12, 1849, aged 62. The following letter written by
James to his friend J. R. McClean will show better than any
words the relationship that subsisted between father and son.

"Jan. 26, 1849.

The loss of our much loved father is the cause of great
sorrow to all of us. On me, who was so dependent on him, this
calamity falls very heavily. He was the chief object of my love,
and my main adviser and supporter in all difficulties. He partici-
pated and sympathized in all my joys and sorrows, and was the
most intimate, as well as the dearest friend I had."

When Lord Kelvin, then over eighty years of age, was installed
* MacLehose and Sons.

RELIGIOUS SCKUPLES XXXIX

as Chancellor of Glasgow University in November 1904, it was
to the remembrance of his father that he turned for the keynote
of the eloquent, though simple, address he gave to the students,
and to the large company assembled to do him honour.

One of the few old students of Dr Thomson now surviving,
namely, Professor Jack of Glasgow, in a recent speech* made
appreciative reference to him as follows :

" In my first year at College, I took Latin with Ramsay, Greek
with Lushington, and Mathematics with James Thomson, Lord
Kelvin's father. Lord Kelvin, then a lad of 24, had returned
from Cambridge two years previously, as our professor of Natural
Philosophy. During my first session, in January, James Thomson
died, so that I spent only a couple of months under him. But
I vividly remember the gracious and dignified old gentleman,
who kept excellent order, and who impressed me greatly as a wise
and luminous teacher, in friendly and sympathetic touch with
all his students."

After a short visit to his sister Anna, Mrs William Bottomley,
at Fort Breda near Belfast, James went in 1849 to London, staying
in rooms in Westminster. About this period he had to pass
through severe mental struggles before he reached the resting
place of his faith. From this faith he never wavered. It enabled
him throughout his long and useful life to face bravely anxieties
and sorrows ; to deal firmly and gently with wrong-doing on the
part of others; and to lead a life of unswerving righteousness
himself; and, finally, to meet death without dread or horror, it
might almost be said with cheerfulness. For some time previous
to his father's death he had felt that his reason compelled him to
reject much that was then considered essential in the faith in
which he had been brought up. He had to a certain extent
opened his mind to his father, but had not ventured to explain
his views concerning religion to his brothers and sisters. To
unburden his mind to them would, he knew, cause intense
distress, and might lead to a rupture of the family affection
which bound them all so closely together.

But to a man so open and conscientious concealment of any
kind was distressing. He therefore made up his mind to com-
municate to his brothers and sisters and his most intimate friends
William Ker and Robert Douglas, his change of opinion, and

* October 26th, 1910 on the occasion of the presentation of his portrait in
Glasgow, on retiring from the Chair of Mathematics.

xl BIOGRAPHICAL SKETCH

abide the consequences. The draft of the following letter was
found among his papers after his death ;

To Robert Douglas:

" 16 FLUDYER ST., WESTMINSTER.
March 3, 1849.

...And now, my dear Robert, as you have hitherto been one
of my most intimate and most loved friends, I must tell you the
reason of my leaving home at this time. It is, that my religious
opinions differ much as to facts, though I hope not much in spirit,
from those of most of my friends. When my father died, I felt
that I could not live longer with the other members of our family
withholding from them my real sentiments, and I thought that,
if I disclosed them, it would probably be necessary for me to live
away from home. On this account, however painful the effort
was, and gloomy the prospect before me, I tore myself away
from my friends; and on arriving in London, I made the whole
case known to those of our family, who are in Glasgow and in
Belfast; but I have since received letters from them indicating
such a spirit of true kindness and love on their part as has made
me quite happy.

I believe, then, in one God the Creator, the Preserver, and
the Governor of all other beings; and I believe that He has
given us, while we are in this world, no other revelation of
Himself but that contained in His wonderful works, and in the
ideas which He has implanted in our minds, or rather which He
has adapted our minds to receive.

I think we should never neglect to pray to Him, and we
should keep constantly before us the idea expressed in the words
' Thou, God, seest me.' I thus see that much is left in obscurity
to us in our present state ; but I firmly hope and trust that when
we die we shall enter into closer communion with our Maker."

As might have been expected, this simple straightforward
confession tended rather to endear the man to those who already
knew and loved him, than to give rise to any estrangement; but he
continued to live in London working with Professor Lewis Gordon.

In 1851 he decided to accede to his sister Anna's earnest
request to come and settle as a Civil Engineer in Belfast, where
conditions were more favourable for his inventions, coal being
dearer and less used than in England, and water power more
available. Here he opened an office for engineering practice,
and very soon found himself among a large circle of congenial
people. His brother-in-law, William Bottomley, was a member
of the Literary Society of which his own father had been

EARLY SCIENTIFIC ACTIVITY IN BELFAST xli

President in the year 1821 — 2. There he would meet many
friends of his father, as well as younger men who had joined
after the Thomsons moved to Glasgow ; among others the Rev.
John Scott Porter, whose writings and preaching attracted much
attention, and whose son, Andrew Marshall Porter (now Bart.),
was afterwards the very distinguished Master of the Rolls in
Ireland; the two brothers Murphy, Isaac and Joseph John;
Dr Neilson Hancock of whose sister we shall hear more anon ;
and Professor Thomas Andrews with whom James Thomson
afterwards did some of his most important scientific work.
Elected a member in 1853, James Thomson became President
in the session 1864 — 5, and honorary member on leaving Belfast
in 1873.

He read to the Society the following papers :

March 5th, 1855.— On the Parallel Roads of Glen Roy;

May 14th, 1855. — On various plans for warming rooms and

buildings ;
Feb. 8th, 1858. — On Work and Power; their measures and

measurement ;

Jan. 10th, 1859. — Ventilation of Apartments ;
April 2nd, I860.— The Theory of Perspective;
Feb. 1st, 1864.— On Bridges and Tunnels ;

Jan. 7th, 1867. — On Strength, Safety and Danger of Structures;
March 6th, 1871. — Explanations and Illustrations of Hydraulics.

Some of these papers have never been published, and their
titles are given here to show the kind of work that occupied him
in Belfast.

In 1851 a new society, called the Belfast Social Enquiry
Society, had been formed, of which Dr Neilson Hancock, who
held the Chair of Political Economy in Queen's College, was
Secretary, and William Bottomley was Treasurer. It was before
this Society that James Thomson read a remarkable paper on
Public Parks in connection with large towns, on March 2nd, 1852.
(See No. 66, p. 464). In it he explained a scheme by which
a growing town can provide public parks for the benefit of the
community, the money for the purpose being obtained by taxing
the land surrounding the town while it is increasing in value.
This paper led directly to the purchase, for the town of Belfast,
of the large Ormeau Park. Many years later, when he was

T. ^

xlii BIOGKAPHICAL SKETCH

President of the Belfast Engineering and Architectural Associa-
tion, he put forward in his presidential address a strong plea for
the State Purchase of Railways in Ireland. (See No. 67, p. 472.)

To the Belfast Natural History Society he communicated
much on the newest scientific thought of the day in addition to
reading papers of his own. One of these read on April 1, 1857,
on " Capillary Motions Observable on the Mixing of Liquids "
contained the views he had expressed two years before at the
British Association in a paper entitled "On Certain Curious
Motions Observable at the Surfaces of Wine and other Alcoholic
Liquors "(No. 21, p. 125).

On the 13th January 1869, he read another paper before this
Society on " Capillary Phenomena as influenced by Temperature,"
and on the 6th April 1870, "Illustrations of the Diffusion of
Liquids"; but no reports of these papers are available.

In 1863 he became one of the original members of the Belfast
Naturalists' Field Club of which he was elected Chairman in 1868.
His most important contribution to its proceedings was the paper
on the "Jointed Prismatic Structure of the Giant's Causeway"
read in 1869. (Cf. No. 62, p. 422.)

He was a member of the Institution of Civil Engineers in
Ireland, and in 1871 wrote for it a paper on the Jet Pump
with Intermittent Reservoirs for the drainage of flooded lands.

He was a well-known figure at the meetings of the British
Association, which he attended as regularly as possible from 1850
onwards, and he was President of the Mechanical Section at the
Belfast Meeting in 1874.

Some account of his original work up to this time may now
be inserted. When studying the utilization of water power by
turbines, he investigated the actions in a Free Vortex or, as he
named it, " Vortex of Free Mobility " and he read an account of
this new departure in exact hydrodynamic observation and theory
at the meeting of the British Association in 1852 of which no
full report is preserved. The short abstract is given below
(No. 1, p. 1). It will be remembered that Helmholtz's great
Mathematical Memoir on the general properties of Vortex Motion
appeared in 1858.

A full description of the Vortex Turbine was read at the
same meeting of the British Association and was printed in
extenso with the Reports (No. 2, p. 2). In 1854 he read another

CENTRIFUGAL JET PUMP xliii

paper on Centrifugal Pumps, of which no report is preserved;
and in 1855 a paper on a windmill and centrifugal pump (No. 3,
p. 16). The best description, however, of his improved centrifugal
pump with exterior whirlpool is to be found in the paper read
before the Institution of Engineers in Scotland on 27th October
1858 (No. 4, p. 16).

Two other important lines of thought that interested him
in later years come directly from his work on turbines and
centrifugal pumps, viz. improvements in the friction brake dyna-
mometer, and improved methods of measuring the flow of water.
He contrived the jet pump in order, as he says in a note, to drain
the pits of his turbines when this was required for purposes of
cleaning: see the paper at the British Association of 1852
(No. 6, p. 26).

Experimental results showing the efficient action of the jet
pump were given at the British Association in 1853 (No. 7, p. 27).
A subsequent paper, read before the Royal Dublin Society on
1st June 1855 (No. 8, p. 30) gives a further development of this
invention, viz. the provision of a series of jet pumps for use in
draining swamps, so arranged that more or fewer could be used
according to necessity. His own words, in a paper read before
the Chemico- Agricultural Society of Ulster in 1859, may be
quoted :

" Now, it is to be observed that the jet pump cannot work at
all with less than its full supply of water. A simple Jet-Pump
is therefore not suitable for working on a varying stream of water.
For the drainage of lands, however, it is proposed that a series
of Jet-Pumps should be so combined as that one, two, three, or
more of them will come into action according to the amount of
water supply flowing at any particular time. This is effected by
placing any number of them, such as four or five, in a row under-
neath their supply cistern, and arranging the inlets for the wate r
to them in such a way that when one has got its full supply,
whatever surplus water there may be shall flow on to the next
of them, and so forth with the others of the series."

In this paper he further stated :

" That a jet pump had recently been erected by William
Forster, Esquire of Ballynure, near Clones, a member of this
Society, for draining a portion of the wet lands adjacent to his
house; and that the performance of the pump in raising the
water had been found to be fully successful,"

xliv BIOGRAPHICAL SKETCH

He exhibited to the meeting various drawings explanatory
of the principles and mode of application of such pumps; also
drawings of the pump on Mr Forster's estate : and his explana-
tions were illustrated by a working model.

A later paper entitled " On a new application of the jet pump
by steam " read at a meeting of the Belfast Natural History and
Philosophical Society on 21st December 1864 (No. 9, p. 34),
illustrates his capacity for observing and noting facts, and his
power of turning known facts to use in new directions. The last
paper on this subject is the one referred to above (communicated
to the Institution of Civil Engineers in Ireland in 1871), on the
Jet Pump with Intermittent Reservoir for the drainage bf flooded
lands or shallow lakes. After a description similar to that given
in previous papers he continued : —

"Now since the jet pump, when wanted to be applied for
drainage, must be made large enough to do the work of flood
times, it would be quite too large to work continuously in dry
weather; and, therefore, it is made to work intermittently, by
the arrangement in conjunction with, it of an intermittently
flowing reservoir. The reservoir is made to receive the continuous
but variable supply of water for power coming from the higher
ground, and to give it out intermittently to the jet pump. The
intermittent action is brought about in a very simple way by
means of two syphons, the smaller being used to start the larger."

His professional work in designing turbines, and his duties as
engineer to the Belfast Water Commissioners, led him to study
the measurement of water in rivers and streams. The first com-
munication on this subject, read before the British Association in
1855 (No. 10, p. 35), merely relates to the experiments made by
Poncelet and Lebros at Metz in 1827 and 1828, and gives some
practical details that should be attended to in order to obtain
accurate results.

Having been commissioned by the British Association to make
further investigations, he presented a preliminary report in 1856
which is not here reproduced. In the report which he presented
in 1858 (No. 11, p. 36) he made a great advance by proposing
the use of triangular or V notches in the weir board instead of
rectangular ones. Notches of this form are amenable to exact
calculation, because the issuing jet is of the same shape whatever
be the extent of the notch that is occupied by the stream. In fact
he deduced the law that the quantities of water flowing through

GAUGING OF WATER xlv

similar notches are proportional to the 5/2 power of their linear
dimensions.

Another report to the British Association in 1861 (No. 12,
p. 42) gives the result of further experiments for determining the
single numerical coefficient that is involved in the formula for the
V notch. The work on this subject is summed up in the paper
which he gave to the British Association in 1876 (No. 14, p. 56).

These experiments were all made at trifling cost with simple
apparatus on a stream in the open air. It is interesting to note
that an important set of experiments made with great care and
accuracy, in 1909, in the new James Watt Laboratory, in Glasgow
University, by Mr James Barr (under the supervision of Prof.
Archibald Barr), while revealing effects due to the bottom and
sides of the stream, and to the smoothness or roughness of the
weir board, has yet confirmed in a remarkable degree this early
work of 1860. Mr Barr says*:—

Dr Thomson gave *305 as the average value of the coefficient
c for heads ranging from 2 to 7 inches. Figs. 21 and 24 show
how remarkably near this may have been to the true value for
the gauge notch which he used. It is a proof of Dr Thomson's
genius as an experimenter that, with the crude apparatus at his
disposal, he was able to arrive at such an accurate result.

The necessity for accurate measurement of power led Thomson
to study the friction brake dynamometer, and he read a paper
before the British Association in 1855 of which an abstract is
given below (No. 5, p. 24). The dynamometer submitted to
that meeting was put aside for many years on the ground mainly
that he "could not see how to work out the principle in an
apparatus cheap enough and simple enough for the occasional
uses for which such dynamometers are ordinarily applied." Later,
he devised a new form of dynamometer or ergometer, and con-
structed a small working model which he showed from year to
year to his classes in Glasgow University. It comprised fast and
loose pulleys on a shaft, and a rope, attached to the loose pulley,
lapping partially round the fast pulley, with weights at each end.
The loose pulley adjusted itself to give the requisite arc of
contact, winding or unwinding the cord on the running pulley
as required for adjusting the resistance. He did not formally
publish this invention, but in a letter to Engineering, 29 October

* Engineering, Vol. LXXXIX. April 8th, 15th, 1910. pp. 435, 473.

xlvi

BIOGRAPHICAL SKETCH

1880 (Vol. xxx, p. 379) he claimed to have had it in public
use in November 1879, and also to have devised and tried a
regulator for preventing oscillations in the loose pulley and the

two weights. The principle of
this regulator "consists in intro-
ducing what is equivalent to
adding inertia without adding
weight to the lighter of the two
weights of the ergometer. The
inertia is applied by connecting
a small and finely pivoted fly
wheel to the lighter weight, so
that the fly wheel revolves
forward and backward with a
varying velocity always pro-
portional to the downward or
upward velocity of the lighter
weight. Inertia accompanying
the motion of the heavier
weight I judge by theory, con-
firmed by experiment so far as
experiments have gone, is in-
jurious as to attainment of

steady action in the ergometer ; and unfortunately the loose drum
introduces inertia injuriously in this way. But, on the other hand,
inertia accompanying the motion of the lighter weight I judge by
theory to be very beneficial ; and my practical trials, so far as they
have gone, seem to confirm this theoretical view, and to show inertia
introduced in that way to be very remarkably beneficial in pro-
ducing steady action without entailing any vitiatory conditions*."

In the discussion of the paper on Engineering Laboratories
read before the Institution of Civil Engineers on 21st December
1886 by Prof. Kennedy •[•, Prof. Barr described Thomson's Dynamo-
meter and gave the illustration of it here reproduced. Prof. Barr
said, "It was shown by Prof. Thomson to his class ; some years
before it was published by Carpentier, and it was used at the
Glasgow Gas Exhibition (1880) for testing on the very day on

* The inertia wheel is regularly used, with most beneficial effects, on friction
brake dynamometers in the James Watt Laboratories in Glasgow University,
t Proc. Inst. Civ. Eng. Vol. LXXXVIII. pp. 109, 110.

FRICTION BRAKE DYNAMOMETER xlvii

which a description of it was published in this country. He
believed it was the only brake which could apply an absolutely
uniform resistance." On a later occasion Professor Ayrton said* : —
"Another plan was to vary the arc of contact. It was curious
that every person who had arrived at that idea seemed to regard
it as his own. It had been invented over and over again.... He
believed it was due initially to Professor James Thomson."

On the 20th November 1888, in a discussion at the Institution
of Engineers and Shipbuilders in Scotland on the Horse Power of
Marine Engines, Professor Thomson said : —

"That he placed no confidence in the numerical expressions
put forward under the name of nominal horse power. He had
always felt that such an expression was rather misleading than
helpful. He was in favour of improving the means of ascertaining
the actual power of the engine delivered at its own shaft, and
dealing with that power rather than with the power given to the
driving piston or pistons by the steam. He thought there was a
possibility of measuring the power by the elastic yielding of the
shaft under the torsional forcive action or torque to which it is
subjected, a method that had been proposed by Him, and which
was to be found mentioned in one of Rankine's books f. He had
himself, conjointly with his son, about eight years ago, proposed
essentially the same mode of measurement of power, without then
knowing of Hirn's invention or publication in this matter, though
they found it soon after as described in Rankine's treatise. Their
own contrivances differed importantly in some of the mechanical
arrangements from those of Hirn, and their intentions included,
further, the application of the general principle to the measure-
ment of power in screw propelled steamships, and more especially
in their speed trials, with a view to obtaining improved data for
ship design. Their intentions related also to the obtaining of
trustworthy records of the varying violences of torsion applied
during long voyages by the waves and engine jointly to the
shafting, as such information would be valuable with a view to
the better determination of strengths for propeller shafting, and
so to the abatement of breakages at sea."

William John Hancock, the father of Dr Neilson Hancock,
who has been mentioned above, had been land agent on Lord
Lurgan's estates for many years, and was subsequently appointed
Poor Law Commissioner at the time when the new Poor Law was
introduced into Ireland. He literally laid down his life for the

* Proc. Inst. Civ. Eng. Vol. xcv. p. 54.

f Kankine, Machinery and Milhvork § 344, p. 387, " On the Torsion Dynamo-
meter of M. G. Hirn."

xlviii BIOGRAPHICAL SKETCH

poor and suffering, in the year of the terrible epidemic of typhus
fever which followed the famine of 1847. In exerting himself to
try to minimize the hardships of the poor patients in the over-
crowded workhouse hospitals he himself had contracted the fatal
disease. His eldest son, John Hancock, had attended Professor
James Thomson's classes at the Academical Institution at the
same time as William Bottomley, and when the younger brother
Neilson was appointed to the Chair of Political Economy at
Queen's College, Mr and Mrs Bottomley visited his mother with
whom he lived. His only daughter, Elizabeth, a bright intelligent
girl who had been his companion during his lifetime, and was
then her mother's chief helper, soon became an intimate friend
of Mrs William Bottomley. James Thomson, who was constantly
at his sister's house at Fort Breda, thus had many opportunities
of meeting her friend. Acquaintance ripened into friendship.
Elizabeth Hancock's mother was a woman of unusually broad views
for that time, and she had brought up her children in such a way
that her daughter had no difficulty in reconciling James Thomson's
creed with her own. When Dr Neilson Hancock was appointed to
Archbishop Whately's Chair of Political Economy at the University
of Dublin, Mrs Hancock decided to leave Belfast and join her son.
James Thomson found it very pleasant to help Miss Hancock to
pack up her brother's books, and before she actually left he
discovered that her presence was necessary to his happiness. They
became engaged in the autumn and were married in Lurgan
Church on December 28th, 1853. Their honeymoon, spent at
Bryansford at the foot of the Mourne Mountains, in a little inn
where they were nearly snowed up, was cut short by a request
from Queen's College, Belfast, that the young engineer would fill
the office of Professor of Civil Engineering during Professor
Godwin's temporary absence, an offer that was gladly accepted in
the hope that it might lead to something permanent. This hope
was fulfilled in 1857 when he was appointed to the Chair.

A happier marriage could hardly be imagined. Mrs Thomson
devoted herself to her husband and to their three children. He
relied on her help and sympathy in his own work for the various
Societies to which he belonged, while she enlisted his sympathy
for the many public movements, such as the higher education of
women and the Married Women's Property Act, to which she
gave her mind in later years. The young couple found themselves

MARRIAGE xlix

immediately in the centre of a large social circle, as they were
both well known and much liked in Belfast before their marriage.
One of their friends was George Fuller (the younger brother of
Frederick Fuller of Cambridge, afterwards Professor at Aberdeen),
who came to Belfast as assistant to James Thomson soon after the
latter opened his own office as an Engineer. This was the com-
mencement of a friendship which lasted through life. George
Fuller, who was best man at his wedding, later on went to India.
He and Thomson carried on a very interesting correspondence,
and when James Thomson left Belfast in 1873 to occupy the
Chair of Engineering in the University of Glasgow, Fuller suc-
ceeded him as Professor in Belfast.

About the time of his marriage James Thomson was appointed
Engineer to the Belfast Water Commissioners, and he was from
time to time consulted by various public boards in the North of
Ireland with regard to the water supply of their towns. Meanwhile
William Thomson had married Margaret Crum of Thornliebank,
nearly a year before James married Elizabeth Hancock. William's
last letter to his brother before his engagement may well be given
here : —

"32 DUKE STREET, ST JAMES'.

Monday, June 21, 1852.

I arrived in London I believe this day fortnight, and ever
since I came I have been very much engaged with seeing people,
looking after instruments etc. I have not yet had time to do
almost anything in the way of sightseeing and other London
strangers' occupation. I have seen Faraday, Col. Sabine, and
others of the ' savans ' a good deal, and I was admitted as Fellow
of the Royal Society at one of the meetings, which are now over
for the season.

On Saturday last I had 3 hours talk with Faraday, and
immediately after had a visit from Mr Tyndall (who has experi-
mented and written on magnetism etc.) which lasted for about
two hours. I found it very curious to compare the sort, of
arguments which had effect on the two, each considering as
utterly unintelligible or inadmissible arguments on a certain
point with which I believe the other was satisfied; and I think
I succeeded in convincing them both of one conclusion which was
contradictory to a good many assumptions that they and others
had been making. I lived with Sylvester for four or five days
after my arrival in town, during which time we had perpetual
conversations, either on his algebraic investigations, or on the
subjects of some of my papers on electricity and magnetism which
he has been reading.

1 BIOGRAPHICAL SKETCH

Stokes lodged along with me for a week, and we used to go
together very frequently to Barker's (the optician) in Lambeth,
always passing through Barton Street going and coming. I called
at No. 9 one day and heard that Mrs Turnbull had been having
an addition to her family. She was to leave that locality almost
immediately.

I suppose you have heard of Stokes' great discovery in optics,
but whether or not, I must delay telling you anything of it till I
see you.

I was surprised last Friday morning to receive a great packet
by post from Paris, which I found contained a proof sheet of my
two papers on the Dynamical Theory of Heat, translated into
French for Liouville's Journal. I have had rather a heavy job
correcting it, and have not nearly done yet. I have a greafc many
projects of papers to write and a few actually in progress, so you
may conceive that my hands are pretty full....

Talking of babies, Mrs Joule has had a second which is a girl,
notwithstanding which I am asked to be its godfather ; so I have
an addition to my family of godchildren which is now tolerably
numerous."

Another letter from William Thomson may be quoted here :
"PHIL. Soc., SATURDAY, Jan. 13, 1854.

Did you see that I have applied for a patent, with Rankine
and John Thomson, for an improvement on telegraphic conductors !
I accidentally got on the theory of the propagation of electricity
by submarine wires, one day in October before leaving Largs,
which showed me at once what would be necessary to ensure
efficiency for great distances (300 miles or more) which led to
this, Rankine having suggested the plan of taking a patent, which
I had no idea of at first. In a few days I expect it will be secured
to us : in the meantime don't say even- as much as I have said to
you, on the subject. I am not very hopeful of making anything
of it, but it is possible that it may be profitable."

During the twelve years that elapsed till the splendid enter-
prise came to a successful issue in 1866 and the Atlantic Cable
was an accomplished fact, and during the repeated trials and
supposed failures described so graphically by Prof. Silvanus
Thompson in his Life of Lord Kelvin, James Thomson watched
and waited full of hope and anxiety, ready at the slightest signal
to give his brother any aid in his power; and great indeed was
his joy when the news came from mid-ocean through the Great
Easterns cable that all was well.

These years were among the most strenuous in the lives of
both the brothers; and whenever a new idea or principle or

REMINISCENCES OF HIS WORK AS PROFESSOR li

invention occurred to either of them he would send off a note to
the other, reserving a deeper discussion of the subject till they
had an opportunity of meeting. Some of the letters from William
to his brother are written on fly leaves of his manuscript " Green
Book " ; one is written from the ss. Elk off Carrickfergus on the
backs of two hotel advertisements borrowed from the steward on
board.

One of his most brilliant Belfast pupils, Professor John Perry,
F.R.S., has put on record* Professor Thomson's method in dealing
with his class : —

" As one of Professor James Thomson's pupils, I may say that
he was one of the kindest of men, with a very strong sense of
duty. He was always nervously anxious that his pupils should
have correct notions of the scientific principles of engineering
methods. He was, in fact, a pure-minded man, whose good
influence is now widely felt, as I have met his pupils in all parts
of the world. Every one of us could laugh at his well-known
foibles, but, however great or small we might be, there was
not one of us who had not a loving memory of him as dis-
tinguished from a mere liking and from mere respect. We all
respected him.

What is especially interesting in his career, is that he did not
publish much — but everything he published was of sterling im-
portance to the physicist and engineer, and no one has ever had
to correct his results. Take one branch of engineering, for
example, hydraulics. In any treatise on practical hydrodynamics
there is a great parade of mathematical calculation ; but beyond
the simple equations relating to pure fluids, what is there that
can really be relied upon by the engineer except the few
propositions so thoroughly proved by Professor James Thomson ?
What a mass of mathematics there is to be found upon the
gauging of water — but is there anything demonstrated, anything
that the engineer can rest upon as a principle in this subject,
except Professor James Thomson's proposition concerning the flow
from similar and similarly placed orifices ? Two deductions from
this are the rational formulae concerning triangular and rectangular
gauge notches. Again, he, as early as 1847, applied Carnot's cycle
and first principles to the study of the pressure and temperature
of melting ice, and he may be said to have really shown to
Clausius, Rankine, and his brother (Lord Kelvin) the method of
attack which has led to the development of thermodynamics.

I will relate one incident to illustrate Professor Thomson's
sense of duty. In 1870 I was a student at Queen's College,
Belfast, and about to go up for my engineering degree examination

* Industries, 13 May 1892.

Hi BIOGRAPHICAL SKETCH

to Dublin. Now, I had not particularly cared to obtain a degree,
and I had neglected to prepare at the college the requisite show
of drawings. But at a time when he much needed a holiday, he
took the trouble of going to my house and afterwards to the
Lagan Foundry, having heard that during my apprenticeship there
I had made many drawings. He spent a long time examining
them, and made such a report to the University authorities as
caused them to put aside their rule in my particular case. Now
this is not all. It was found subsequently that my attendances at
his classes were not up to the standard, and he utterly refused to
give me the certificate which would enable me to go in to the
examination. It was, in his opinion, wrong to do this ; and, in
spite of a battery of persuasive argument brought to bear upon
him by Dr Andrews and others of his colleagues, his refusal
was absolute. The difficulty was got over through some newly
discovered technical right of the President of the college to
exercise grace. Taking the two incidents together, they may be
regarded as unprecedented in the history of the professorial sense
of duty."

As further illustrating his methods, it may be remarked here
that he constructed a sliding balance, by the use of which the
examiners could mechanically place the students according to the
marks gained in class and during examination, thus eliminating
any possibility of favouritism or prejudice in deciding the results.

In the autumn of 1861 James Thomson and his wife and six
year old daughter spent ten days very happily with Prof. William
Thomson and his wife on the Island of Arran, where the William
Thomsons had rented for summer quarters a small country place
called Kilmichael, the only part of Arran not belonging to the
Duke of Hamilton. There were two other guests staying at
Kilmichael, namely Dr Joule and Prof. Forbes, and endless
discussions arose among the four at table — where so unimportant
a matter as food was liable to be entirely forgotten — or out boating
on the lovely September evenings. Sometimes the conversations
on deep questions of science, such as the effect of stresses in causing
the melting of solids, became so absorbing that one or more of
them forgot to row, while the others, not perceiving the omission,
continued rowing steadily, so that the boat went round in graceful
gyrations or loops and circles, in spite of the steerswoman's efforts
to keep a straight course. One evening when the sea was quite
smooth except for small ripples, they noticed long sinuous streaks
of perfectly calm water among the ripples, and, rowing out to the
spot to investigate the cause, James Thomson pointed out to the

EXPLANATIONS OF PHYSICAL PHENOMENA liii

others that these calm lines were caused by small floating objects,
bits of seaweed, withered leaves, etc., which collected at the place
where two currents met and perforce the water had to descend,
leaving the small floating particles on the surface at the line of
meeting, where they had the effect of deadening the tiny wavelets
and thus caused the calm line. His explanation is developed in a
paper read before the Belfast Nat. Hist, and Phil. Society on the
7th May 1862 and published in the Philosophical Magazine,
(No. 25, p. 142). This paper was reprinted long afterwards as an
appendix to one read in 1882 before the Phil. Society of Glasgow
on " Changing Tesselated Structure in Certain Liquids " (No. 24,
p. 136), which he traced in a most interesting and suggestive
manner to a vertical circulation establishing a sort of cellular or
rather columnar pattern of convection currents.

The subject of the melting of ice under pressure led to
important developments with regard to geological questions,
besides its application to glacier motion already referred to. It
brought him into friendly relations with Faraday and with
H. C. Sorby, and the scientific correspondence which ensued is
printed infra, p. 212 and p. 252, in its natural sequence. His
brother William, writing to J. D. Forbes on August 20, 1860,
sums up as follows : —

"His (Faraday's) 'experiments' are beautiful. But I think
the results are in very strong accordance with my brother's view.
The first contact between the convex blocks takes place at a mere
point, and with a slight impact. It must therefore give rise to
considerable internal stress in a very small part of each block.
This, according to my brother's theory, is enough to make the two
freeze together on the ceasing of the instantaneous pressure.
After they are thus united, the tension which Faraday applies
and keeps applied tending to separate them, will raise the
temperature at which the solid neck or isthmus joining them
could melt; it will also instantaneously raise the actual tem-
perature of the ice-isthmus, and tend to thin it viscously
(according to my brother's explanation of the viscosity of ice).
But unless it is strong enough to crack or quickly thin down to
nothing the isthmus, and so separate the pieces again, the
temperature of the isthmus will very quickly sink to that of
the surrounding water — viz. 32° Fahr. — then there will be an
isthmus of solid at a temperature below its proper freezing point,
constantly washed, for hours and days, by liquid of the same
composition which therefore cannot but freeze upon it and render
it thicker and stronger as in Faraday's experiment."

Hv BIOGRAPHICAL SKETCH

The following letter refers to a controversy with Prof. Tyndall
on the same subject.

"2 DONEGALL SQUARE WEST, BELFAST.
1st Oct. 1861.

MY DEAR WILLIAM,

...In a letter which I wrote to you on the 1st of
Aug. 1861, I said that I was not sure whether in a vortex of free
mobility, extending outwards to an infinite distance radially, but
which I meant to be of a finite thickness as measured parallel to
the axis of rotation, the mechanical work required to generate the
motion would be finite or infinite ; but that I thought it would be
easy to calculate this. I have now made the investigation for
that purpose, which comes out quite easy, and which I think is of
interest, and I enclose to you a copy.

I have also written out, a little more distinctly than when I
was with you, the statement of the general principle which I think
holds good — and of which I think my view of the effect of stresses
in causing crystals in their melted fluid, or crystals in their
saturated solutions, to melt or dissolve on the application to them
of stresses tending to change their form, is a particular case. If
you can readily let me know your opinion of this axiom or general
principle, I shall be glad to receive it. If you think the principle
is correct and the statement of it good, I would probably introduce
it into my intended paper for the R. S., on the effect of stresses
tending to change of form on crystals in their molten fluids or in
their saturated solutions*. I met Dr Stevelly yesterday and he
had seen Tyndall at the British Association.... He told Tyndall
that I had succeeded in squeezing crystals of wet salt into a hard
mass, or something to that effect.

Joseph John Murphy f is just home from Switzerland. He
tells me that he saw Tyndall on the Eggischorn, and that they
spoke together as to my views of ice, and that J. J. Murphy said
he thought Tyndall had quite misunderstood my view, and that
Tyndall replied : ' Oh, well, if Mr Thomson thinks so, let him
explain.' This makes a little more reason for publishing my reply
to Tyndall....

Your affte brother,

JAMES THOMSON."

During this autumn he suffered from sleeplessness and was

advised to take complete rest from College duties. He went to

Dublin to stay with his brother-in-law, Dr Neilson Hancock, and

meantime Dr Andrews kindly undertook to conduct his classes.

A most interesting and remarkable correspondence took place

* See infra, p. 236.

f Author of a notable book Habit and Intelligence, and an early writer on
evolutionary subjects.

EARLY IDEAS ON AVAILABLE ENERGY lv

on the limitations of the law of dissipation of energy, and the
influence of vitality on matter, which is here given in full.

"2 DONEGALL SQUARE WEST, BELFAST.
April 1th, 1862.

MY DEAR WILLIAM,

According to the Theory of Thermodynamics which
you and others have lately worked out and adopted, it appears
that 'although mechanical energy is indestructible, there is a
universal tendency to its dissipation, which produces gradual
augmentation and diffusion of heat, cessation of motion, and
exhaustion of potential energy through the material universe '
(quoted from your writings, see 'On Age of Sun's Heat*'). I
understand that you consider that when mechanical energy dis-
appears, it is replaced by an equivalent amount of vis viva in the
molecular or other motions, which are supposed to constitute heat;
and that while man can apply mechanical vis-viva, or mechanical
energy of motion (by which terms I mean to express the energy of
the motion of bodies of finite size or of size decidedly larger than
what can be regarded as molecular ; and to distinguish it from the
energy of such motions as may be supposed to constitute heat), so
as to produce potential energy, he cannot possibly turn to such
account, by any actions of matter on matter induced by him nor
in any way, the vis viva of heat, if the heat he has at command be
all at one temperature : also that he can obtain potential energy
from heat only through allowing other portions of heat at different
temperatures to equalise themselves in temperature, and that so
the continual tendency of man's obtaining potential energy from
differences of temperature and expending it, must be towards
bringing about a state of uniform temperature from which it
would be impossible for him to obtain potential energy again.

With the foregoing I am quite disposed to agree, except that
I think it may perhaps be necessary to qualify the theory, or to
qualify what might be taken as implied in it, by excepting from
its decided statements, and leaving as still unknown and uncertain,
the mysterious influence of spirit, life, or the vital principle in
animals and plants over the matter composing their living bod:'os.
I think we must look on this influence as being contrary to, or
predominant over, the ordinary laws of matter. Thus for instance
at any particular moment the molecules composing a living body
are in a certain position and connexion with respect to one
another. They are possessed of much potential energy, and if left
to themselves at that instant without the control of what we call
spirit or life, they would go through certain actions, continually
passing to states of lower potential energy until arrival at some
minimum of potential energy though not necessarily the lowest

* Popular Lectures and Addresses, Vol. i. p. 349.

Ivi BIOGRAPHICAL SKETCH

minimum. (What I mean by this may be understood on con-
sideration that in certain circumstances decomposition or putre-
faction may be arrested indefinitely.) Now when spirit or life,
connected with these material particles, can hinder the actions
which the material particles would of themselves go- through
in virtue of their potential energy, and can cause them to
go through quite different sets of actions, and through sets of
actions which, if we believe in free will, as I do, we must consider
as not following one another in a natural* sequence of cause and
effect according to the physical f laws of matter; as not being
fixed for the future by the present condition in which the matter
exists; and as being absolutely at the command or under the
predominant influence of something which is not matter ; it
cannot be disputed by anyone who believes the mind or life to be
distinct from matter and to be no mere result of arrangement of
particles of matter and of their energies, that the vital principle
has the power of regulating and applying the potential energies of
the matter composing the living body with which it is connected,
so as to keep them from applying themselves as they would do if
left to themselves. This influence of mind or life over matter is
altogether mysterious. It implies I think a perfect suspension or
contravention of the physical f laws of matter; and may be
regarded as a part of a great miracle which constantly goes on
around us (although most people will not call anything miraculous,
unless it be extremely rare, or unless it be unique, so that all the
human race except a very few, must either believe it or reject it
by judging from the testimony of others, or from geological records
of events which have occurred even before the human race was on
the earth).

Now if we allow that mind or life really has the power of
counteracting the physical laws of matter — that is the laws of
inanimate matter — it seems to me to be a perfectly admissible
supposition that mind or vitality may have the power, in the
living body, of collecting, and applying as potential energy, the
energy of the heat motions, or of bringing out in the living body
from the vis viva stored indefinitely everywhere as heat, the
potential energy which you regard as a true equivalent for the
vis viva of the heat, and for which you consider the vis viva on
the other hand to be also a true equivalent. Without asserting
that we have a right to assume that vitality really has that power
of bringing out the equivalent of mechanical energy from an
equivalent of heat (that is of effecting a reversal which by merely
the physical laws of matter is impossible to be brought about)

* I here use 'Natural' and 'Physical1 not exactly as you are proposing to use
such terms. I mean them both to apply to the phenomena of the energies of
inanimate matter.

t I use the term 'physical' here in its ordinary sense at present in common
use ; namely as distinguished from vital or psychological.

VITALITY IN RELATION TO AVAILABLE ENERGY Ivii

I want to guard against what I consider is equally a doubtful
supposition but is yet generally assumed : namely that all the
animal and vegetable energies are derived solely from previous
potential energies, or other energies capable by ordinary physical
means (such as air engines, chemical actions, etc.) of being con-
verted into potential energies. I want to say that perhaps the
vitality of animals and plants may be able to reverse processes
which would go on if not influenced by the vitality. We know, as
I have said before, that the vitality can and does divert the course
of action of energies : does it not then follow that it at least stops
some of their courses of action or even reverses some ? And
farther is it at all incredible that vitality should be able to cause
the passage of heat into what you regard as neither more nor less
than a true equivalent for it, namely, into the Joule's " equivalent "
of potential energy or mechanical energy ? I do not think this
supposition would be at all more wonderful than the one already
generally admitted, that mind has the power of controlling the
courses of energies during their passage to the lower state, or
state of dissipation, and of equivalent augmentation of heat.

I suggest the above ideas for consideration, and I think there
is much in them in regard to which it will be safest to suspend
judgement.

Your affte brother,

JAMES THOMSON.

P.S. I would not have you to suppose that I am against the
prevailing opinion that animal power is derived (or mainly
derived) from potential energies stored in the food eaten and the
air breathed: but what I chiefly want to say is that I do not
think we are entitled to set down as a proved impossibility the
conversion, through vital influence, of heat into mechanical energy;
and I would say may not the impulse of volition communicated
from the mind to the body consist in a reversal of an action or set
of actions in the body, perhaps in the brain or nerves, which
would go on under the ordinary physical laws ; the antecedent and
subsequent conditions, whether in the forward or reversed action,
being (as I believe you say) truly equivalent for one another.
Then when one part of an action is reversed or stopped it is easy
to conceive that the whole remaining course of the actions may be
thereby turned into new channels.

J. T."

"COLLEGE, April 21, 1862.

MY DEAR JAMES,

I have not had time yet to read Mr Murphy's paper
which you sent me, but I hope to do so soon, and to write to you
accordingly.

T. e

Iviii BIOGRAPHICAL SKETCH

Your previous paper on thermodynamics of animals I received
and sent on to Tait. I agree with it on the whole. You will
see that I have excepted plants and animals from any assumption
(founded merely on what we know of inorganic matter) of either
the First or the Second Law. In fact neither can be held to be
an axiom when life is concerned, in the same sense as it can for
dead matter. Life being not perpetually reproducible in a cycle,
the sound objections to assumptions involving the 'perpetual
motion ' are not applicable to the assumption that energy may be
called into existence by free will. But analogy from known facts
renders it probable, (almost certain) that energy is not so called
into existence. This I have stated in an old Article*, Proc.
R. S. E., about 1850 [Feb. 1852].

In my ' Dyn. Theo. Heat ' I except action involving life from
the axiom on which I found the Second Law. Physiology as yet
proves nothing as to whether the 2nd Law is really violated or
fulfilled, although I think it probably is fulfilled, in the vital
processes.

Please answer PoggendorfFs questions (see enclosed letter)
and send back the letter and your answer to me. I have
delayed too long, but I shall forward my own answers along
with yours as soon as I receive yours.

Your affecnte Brother,

W. THOMSON.

P.S. Thanks for your paper on Spiral Springs. I shall return
it if you wish. I must have a copy or copies somewhere.

P. P.S. You should send the separate copies to Faraday, or
others notwithstanding they are F.KSs. I shall be glad to have
one."

In 1863 the British Association met for the second time
at Newcastle-upon-Tyne with Lord Armstrong, then Sir William
Armstrong, as President. Professor and Mrs James Thomson and
their brother and sister-in-law, Dr arid Mrs Neilson Hancock,
joined forces and went over to England to be present. This
meeting left very pleasant memories in the minds of the little
party from Ireland. They were entertained with the other
members of the British Association by the President at a dinner
given in the new Banquet Hall which Sir William Armstrong
had just built at Jesmond Dene, and they saw a great deal that
interested them in the neighbourhood, and as usual met a number

* "On the Mechanical Action of Kadiant Heat or Light, on the Power of
Animated Creatures over Matter; on the Sources available to Man for the Produc-
tion of Mechanical Effect." From the Proceedings of the Royal Society of Edinburgh,
Feb. 1852. Reprinted in Mathematical and Physical Papers, Vol. i. p. 505.

COLLABORATION WITH ANDREWS AND PURSER lix

of their friends. The visit terminated with a tour in the Lake
District, where they all agreed that the natural scenery in England
could hold its own with the beauties of Scotland and Ireland.

Soon after their return to Belfast, Prof. Thomson found his
pleasure in his work at Queen's College much enhanced by the
advent from Dublin of the young, brilliant and distinguished
Professor of Mathematics, John Purser. The delight with which
the three friends, Andrews, Thomson and Purser worked together
in the following years, until James Thomson left Belfast in 1873
on his appointment to the Chair of Engineering in the University
of Glasgow, is best told in Prof. Purser's own words*:

"...But of all my colleagues the one with whom I had the
most congenial intercourse was my friend James Thomson who
held the chair of engineering. Of the scientific men I have
come across he most fulfilled the idea of a philosopher, his
ever-working brain always thinking of the causes of things,
pondering on the why and wherefore of different natural phe-
nomena— why, for instance, the blocks at the Causeway assumed
their characteristic prismatic form, or by what process the solid
ice of the glacier, to all appearance so unyielding, was able to
move along its rocky bed. Most modest and retiring, it was
only on closer acquaintance you realised his original power as
an investigator and the tenacity of his hold on physical principles.
You learned, too, that this same grasp of principles found expression
also in the moral sphere, in a character singularly just, anxious to
carry out at all costs what he felt to be true and right. My
intercourse with him, which continued after he had left us to
take charge of the Engineering School in the University of
Glasgow — indeed, to the end of his life — was to me most
stimulating and instructive. He was far the profounder thinker,
but I knew a little more of the technique of mathematical
analysis, and used to give him pleasure when I pointed out
quicker ways of proving some of the theorems he had discovered.

Both James Thomson and I followed with keen zest the
magnificent results that Andrews arrived at in his renowned
investigations in the early ' seventies,' the investigations on the
behaviour of gases under pressure at different temperatures, and
the great discovery of the continuity of the liquid and gaseous
states of matter. Indeed, it has seldom been the good fortune
of an institution of our modest dimensions to include on its staff
at one and the same time two such wonderfully original thinkers
as Thomas Andrews and James Thomson. And Ulster may well

* Taken from his speech at a dinner given to him at Queen's College, Belfast,
on the occasion of his retirement from the professorship : Belfast News Letter,
Jan. 8th, 1902.

Ix BIOGRAPHICAL SKETCH

be proud of both. Both were Ulstermen born and bred. If his
fellow citizens believed in Andrews, certainly he on his side be-
lieved in Belfast, its energy and enterprise, and was wont to
speak with pride of the old worthies it had produced. He even,
though some of us found a difficulty in following him so far,
believed in its climate, declaring that the Belfast winter closely
resembled the Italian. Such were the men with whom in those
early days my happy lot was cast — men all of them interesting,
some of them, as I have tried to show you, deserving the name
of ' great '."

In 1869 Dr Andrews gave to the Royal Society his famous
Bakerian Lecture on the " Continuity of the Liquid and Gaseous
States of Matter" which closes with the following words x

" We have seen that the gaseous and liquid states are only
distant stages of the same condition of matter, and are capable
of passing into one another by a process of continuous change.
A problem of far greater difficulty yet remains to be solved, the
possible continuity of the liquid and solid states of matter. The
fine discovery made some years ago by James Thomson, of the
influence of pressure on the temperature at which liquefaction
occurs, and verified experimentally by Sir W. Thomson, points,
as it appears to me, to the direction this inquiry must take;
and in the case at least of those bodies which expand in liquefying,
and whose melting-points are raised by pressure, the transition
may possibly be effected. But this must be a subject for future
investigation ; and for the present I will not venture to go beyond
the conclusion I have already drawn from direct experiment, that
the gaseous and liquid forms of matter may be transformed into
one another by a series of continuous and unbroken changes."

Both James Thomson and his brother took the keenest interest
in Andrews' work, and the substantial contributions made by James
to the general philosophical development of this subject are recorded
in several papers.

In 1866 the house in Donegall Square, where he had lived
for many years, was wanted for business sites, and Prof. Thomson
bought a house in University Square quite close to the College.
Finding serious defects in the drainage there, his attention was
directed to the whole question of the drainage, warming, and
ventilating of houses. He read several papers on these subjects
before various societies and public bodies, but complete copies
have not been preserved. An abstract of a paper read on
4th December 1867 is given infra, p. 477. His ideas and principles
have in the main been taken up, and have formed the basis of

VENTILATION AND SANITATION Ixi

many of our modern improvements in these matters. For instance
in those days it was the custom to carry down soil pipes inside
a house and under the floors, and so to join them with the public
sewers, often with very defective connections. Thomson was
among the first to urge the necessity of carrying the soil pipes
through the wall above ground, and letting them enter the main
sewer by a properly constructed trap, clear outside of the house.
It is not generally known that he was the first to use smoke as
a test for defects in house drains. He devised a very simple
method of applying his "smoke test" in a house at Castlerock
which he had taken for the summer months in 1872, and the
idea was quickly taken up by others and applied successfully to
the detection of minute leaks.

In later years he gave renewed attention to the ventilation of
public buildings, taking a patent in 1891 for warming and venti-
lating. The invention consists in the exchanging of old air for
new by means of a mechanism — called the " exchange wheel " —
resembling a fan with septums or blades radiating out from the
axle to the circumference. The wheel revolves within a fixed
casing fitted closely to the circumference at two parts diametrically
opposite, each of them extending through an angular space as
great as that comprised between two of the blades of the wheel.
Thus whether the wheel be standing still or revolving, the two
halves into which the portal is divided by the axle, are always
both closed, each by at least one of the radiating blades ; and, in
consequence, the action of the wheel is not affected by any wind
that may be blowing against the walls of the building. For a
large hall, in addition to the ventilation, a circulation of air would
be maintained by an ordinary fan with a view of preventing the
heavy cold air from lodging in the lower part of the hall, the cold
air being drawn away from the floor by apertures there, or as low
down as may be convenient, and the circulating air would enter
the apartment at the ceiling, or at some conveniently elevated
place, so that the circulation is in the main downward through
the apartment. His death prevented the working of the patent ;
but part of the invention has come largely into use in recent years
for revolving, draught- free doors of banks, hotels and offices.

In the summer of 1867 he was engaged in building a new
weir near Belfast for the Lagan Navigation Company, to which
he was at this time appointed engineer.

Ixii BIOGRAPHICAL SKETCH

Two years later Margaret King, the eldest daughter of his
sister Elizabeth, was married in Edinburgh to the distinguished
physical chemist Dr J. H. Gladstone, F.R.S. The whole of the
Thomson family went over for the wedding, and after the event
they had a delightful little tour through the Highlands.

During the session 1867 — 8 Professors Thomson and Purser
were much interested in watching the progress of Dr Andrews'
far-reaching researches into the different states of matter; the
following letter from his brother, then Sir William Thomson,
shows that he too watched the development with keen interest.

"LARGS, Friday, Mar. 4/70.

MY DEAK JAMES,

...You may tell Dr Andrews that I have four different
reasons for knowing that molecules of water, glass, etc. cannot
be less in linear dimensions than about one 1000th of a wave

length of light : or say about ^r — ^ of a centimetre : or that

2\) x -Lu

there cannot be more than about 16 x 1021 molecules of water in
a cubic centimetre. I am getting a short sensational article on
the Size of Atoms ready for Nature*, Dr King acting as amanu-
ensis. He and Elizabeth came here about three weeks ago, for
his sake, as he had been very poorly. They are in lodgings, but
we see a good deal of them, and are doing all we can to help
Elizabeth to keep Dr King's mind off wearing thoughts.

He proposed himself taking down this article for me as a
mental relief for himself. He came two evenings ago when we
made a beginning, and he is coming again to-night.

Your affectionate brother,

W. THOMSON.

P.S. If you see him (Dr Andrews) thank him for the copy
of his paper which he sent me. I am very glad indeed that it
is now out. It will make an era in science.

P.S. The LL.D.f is owing originally to Blackburn. Rankine
made a very good and appreciative speech in proposing or seconding
and Dr Rainy spoke very warmly."

About this time an exhibition of mechanical and useful arts
for working men was got up in Belfast. It is worth recording,
as it was one of the first movements of the kind started for the
benefit of working men in this country. Prof. Thomson exhibited

* See Lord Kelvin's Math, and Phys. Papers, Vol. v. p. 289; or Nature, Vol. i.
pp. 551—553.

f Degree conferred on James Thomson by the University of Glasgow.

ASSOCIATION WITH LORD KELVIN Jxiii

his Jet Pump and Intermittent Reservoir, and was one of the
judges. The exhibition was a great success.

Meanwhile Sir William Thomson was passing through a period
of great anxiety. His wife had a serious illness soon after her
marriage and had suffered much from that time onwards. She
became much more ill in the spring of 1870, and on the 17th of
June died at Largs, surrounded by her much loved sisters and
brothers. Her death left a blank in her husband's life which
could not easily be filled. He threw himself into his work with,
if possible, greater concentration than ever, arid the letters that
passed between the brothers for the next few years are full of
descriptions of the syphon recorder or designs for the new telegraph
ship Hooper. But before this interesting vessel had been fully
planned, Sir William had found at Cowes and bought his yacht,
the Lalla Rookh. Her first voyage from Cowes was to Belfast
Lough where she arrived on October 16th, 1870, and was much
admired. Prof. Thomson, David T. King, and some of the young
Bottomleys were taken for a cruise to Scotland ; and plans were
made for a longer cruise in the following year. The next year
Sir William Thomson took a party including Professor Helmholtz
for a cruise, and a visit was made to Prof, and Mrs Blackburn
at their beautiful home on the West coast of Scotland. The
following extracts from letters from James Thomson to his wife
give an idea of life on board the Lalla Rookh in the holidays. In
Mrs Blackburn's cabinet of drawings there is a sketch of the group
watching the flight of sea-birds, drawn in her own inimitable style.

" (LocH AILORT), 8th Sept. 1871, OFF ROSHVEN,

Friday morning. On board L. R.

...We had a delightful sail with a pleasant breeze, and
Atlantic waves moderated by shelter from Hebrides and Coll
and Tiree. Then coming up into Loch Ailort (on south side
of which Roshven Mountain and Roshven House, both belonging
to Prof. Blackburn, are) we had shelter against waves from the
Islands of Eigg, Muck, and Rum. Then we came farther up the
Lough inside of Goat Island, and anchored in shallow water in
front of Roshven house. We went ashore and saw Prof, and
Mrs B. and their 3 sons and 1 daughter, also Mr Ferguson*
Lecturer or Demonstrator of Chemistry in Glasgow College, under
Prof. Anderson who is unwell for some years and has been mostly
unable for duty. Also John Thomson f.

* [Now Professor of Chemistry, University of Glasgow.]

t [John Millar Thomson, now Professor of Chemistry, King's College, London.]

Ixiv BIOGRAPHICAL SKETCH

We all went to Goat Island ; and climbed to top. It is very
steep. On top there is a great vitrified fort of quite prehistoric
times. Its walls go round a great enclosure like an Irish fort,
only irregular to fit the rocky hill top. There is a natural grassy
hollow like a shallow bowl in interior. The walls are only a few
feet high, rough and irregular, and of course partly broken by
people and by exposure generally. I have got a good specimen
of the vitrified structure to bring home. It is of lumps of stone
like the sizes of macadamizing stones and paving stones, but I
think mostly under 3 inches thick. I did not break it off, but
got it loose where it had been thrown or taken down the hill.

We arranged last night that if to-day would be fine enough
the Blackburns and their party would come out to the L. R.
and we would all sail in the yacht to Eigg where there* is the
very remarkable lava top called the Scuir of Eigg. The day is
wet and very windy : and I suppose we shall stay partly in the
yacht and partly on shore with the Blackburns : but this will
depend on the appearance of the weather later in the morning
or in the day.

The Blackburn party came on board and have kept their
boatmen waiting till letters be written to send ashore : so I
have written in haste. We bathe every morning. Most of us
swim

We saw some admirable drawings yesterday evening done by
Mrs Blackburn. One was a drawing of a baby cuckoo shoving
the other young birds older than itself out of the nest. She
sketched it while the process was going on, and while she was
watching the proceeding with almost breathless interest. That
original sketch* she shewed us, and also a nicely coloured finished
sketch picture of same, done afterwards on a paper about the size
of a page of this letter. These I think are highly interesting;
very few people have ever had an opportunity to see that pro-
ceeding : and of those few I am very sure no one has been such
an artist as Mrs Blackburn, with such wonderful power to sieze
and represent the appearance seen in its most characteristic
moment...."

" Thursday l±th Sept., 2 P.M., 1871.

In Lalla Rookh, off Easdale Island, and Sell Island, Firth of Lome, in
very nearly the latitude of South end of Mull.

...We set sail from Gair Loch early on Tuesday morning,
with a good favourable breeze, and after great battling against
strong tide flow in the Kyles where we were detained 2 hours,
got almost into Tobermory Bay when the wind fell off completely,
and we were becalmed, and could not get in, but remained floating

* [This sketch is published in Birds from Moidart and Elsewhere by Mrs Hugh
Blackburn : Edinburgh, David Douglas, 1895. Cf. also Nature, 14 March 1872, and
Lancet., 2 July 1892; also Dr Jenner, Phil. Trans. 1788, Vol. LXXVII. pp. 225, 226.]

YACHTING EXCURSIONS WITH LORD KELVIN Ixv

in the Sound of Mull till next morning, the Captain and some
of the sailors taking care to keep us from being carried ashore
by tidal currents, and to be ready for taking suitable action if
wind should come on. On the next morning (Wednesday, yesterday)
we were almost completely becalmed except that we had light
favourable breezes in the afternoon. William during the almost
perfect calm, noticed the very slight speed of the yacht through
the water as being fit to enable him to make experiments on
ripples and waves regarding which he had been making out
mathematical theories and discussing them with Professor Helm-
holtz.

He did it by having a nearly vertical fishing line hanging in
the water ; and observing by himself with aid of W. B. and of me
and of J. T. junr. the conditions as to the mode of spreading of
the waves, and as to the speed of the yacht that he wanted.
He found the results very satisfactory to him : and I think he
finds them suitable for publishing in a paper* he will be writing
in which he has been making some quite new discoveries.

There was very little wind yesterday, and we only got on
about 20 miles when evening came on and we anchored in a
glassy calm in Duart Bay in Mull, where the Sound of Mull
widens for a vessel going Southward. Shortly after we anchored
two herring merchant sloops or wherries were moving slowly about
the bay, one on each side of us, the masters of which kept up for
half an hour or an hour an eloquent conversation in Gaelic across
us. The whole scene was better than could be acted in a theatre.
Our mate understood what they were saying and told us some
of it. One had his ship loaded with herrings which he had
bought in Loch Hourn off Sleat Sound, and was taking them
to Glasgow to sell. I think he had bought them for 5s. the
barrel, from the fishermen and expected to realize £1. 10s. Od. ?
or £2. 10s. Od. ? the barrel for them in Glasgow...."

The gradual refraction of rays of light when passing through
the atmosphere claims the attention of engineers in connection
with levelling operations. James Thomson, dissatisfied with the
existing theories then current, had discussed the subject in 1863
with Prof. John Purser in Belfast, when they agreed that an
investigation by the usual method of rays, did actually, when
pushed to the limit, prove curvature of a ray exactly horizontal in
an atmosphere stratified horizontally, though the transition to this
limit is somewhat perplexing and, in fact, had led to loose and
erroneous statements on the subject. As a result of continued
attention to the problem he sent in 1870 to his brother William
a mode of investigation by means of wave fronts which placed the

* [Cf. Lord Kelvin's Mathematical and Physical Papers, Vol. iv. p. 88.]

Ixvi BIOGRAPHICAL SKETCH

subject in a new light, and which has become fundamental for all
such questions relating to the gradual bending of trains of waves.
This investigation was forwarded by William Thomson to Tait
with the characteristic note : " This wants for perfect validity
only the approval of T ' \ " Tait's letter to James Thomson in reply
is given below (p. 451). The paper containing an account of
Purser's solution was communicated by James Thomson to the
British Association in 1872, and is here reprinted* : infra, p. 441.
In 1872 through the death of Prof. Macquorn Rankine the
Chair of Civil Engineering at the University of Glasgow became
vacant, and Sir William much desired his brother to apply.
Anxious correspondence followed. Prof. James Thomson and his
wife and three children had taken root in their home in Belfast.
The Professor was doing very good and important work with his
colleagues at Queen's College ; his youngest daughter, Bessie, had
passed through a severe illness in the summer of 1870 which left
her permanently delicate ; his wife too had been far from strong
during the summer they had just spent at Castlerock. Living in
Glasgow would be more expensive than in Belfast ; so that unless
the emoluments of the Chair were much greater than those at
present at his command it would be wiser to stay where he was.
Sir William however was able to overcome all these objections.
Finding that his brilliant younger brother really considered him
the best man to fill the vacant chair, the Professor could not resist.
Sir William immediately set to work to promote the candidature.
He drew up a statement of his brother's qualifications, particularly
with regard to practical work, and, as it gives a clear, concise
account of James Thomson's achievements as an engineer in
Belfast, it is here quoted in full.

" Professor James Thomson was a pupil in the Horseley Iron
Works Staffordshire, and afterwards a Pupil of Sir William Fairbairn
at his iron shipbuilding works on the Isle of Dogs. He has been
Professor of Civil Engineering in Queen's College, Belfast, for
15 years. For the last five years he has been Engineer to the
Lagan Navigation in County Down. He was Engineer to the
Belfast Water Commissioners, when pumping steam-engines for
supplying water to the Town were erected under his charge.

* [This method of wave fronts is further developed by J. D. Everett in a paper
" On the Optics of Mirage," Phil. Mag. 4, xiv. pp. 161, 248, March and April 1873.
For the important application to rays of sound see Lord Rayleigh, Theory of Sound,
Vol. ii. p. 288.]

TRANSFER TO ENGINEERING CHAIR AT GLASGOW Ixvil

A water pressure engine for supplying the town of Kilrea with
pure spring water by power derived from a river, was proposed by
him and executed under his superintendence. This was quite a
novel design ; and it has proved in the highest degree satisfactory.

He was inventor and patentee of the vortex turbine, renewed
by Privy Council, and has designed and superintended the con-
struction of many of these wheels now working successfully in
various parts of the world : designed and superintended the con-
struction of several large centrifugal pumps for drainage of sugar
plantations in Jamaica and Demerara : has invented and brought
into practical use the Jet Pump and Intermittent Reservoir for
Drainage of swampy lands. This arrangement has been in
successful use now for many years in County Monaghan near
Clones.

He designed and had executed under his personal superin-
tendence, a flood-sluice-weir on the Lagan River near Belfast, for
the purposes of the Navigation. This, on account of the natural
difficulties and contingencies of weather, was a critical piece of
engineering and required good planning and energetic superin-
tendence. It has proved quite successful.

He proposed an improved method of measuring the flow of
rivers and streams by V notches. He worked out the dynamical
theory of this method ; made the requisite experimental investi-
gations, and published practical rules for allowing of their being
brought into general use. He has had ample practice and
experience in Land Surveying, and Levelling, and has regularly
given field instruction and exercise in this department to his
pupils."

Of the many testimonials that were received, three have been
selected as specimens, those from Professors Helmholtz and Tait
and Dr Joule. The final extract is taken from a private letter
written to Sir William by Dr Andrews, which accompanied the
more formal testimonial.

"BERLIN, I4tk January, 1873.

DEAR SIR,

As you wish to have a statement of my opinion regarding
Mr James Thomson's merits as a scientific investigator and his
qualifications for the chair of Engineering at the University of
Glasgow, I have the honour to answer that I regard Mr James
Thomson as a man of very sound and unusually acute judgement
in questions relating to physical, mechanical, and mathematical
science, and a very extended amount of knowledge in these same
branches. His theoretical prediction of the alteration of the
freezing temperature of water by pressure, was an original idea of
first-rate importance. Also his hydrodynamical considerations, and
their practical applications for the construction of water wheels,

Ixviii BIOGRAPHICAL SKETCH

for his jet pumps, for the theory of oceanic and atmospheric
currents, are of a very original turn of mind, and prove that he
is able to follow out his speculations till to the very fundament of
the question.

Besides I know from personal acquaintance his scrutinizing
way to penetrate into the very heart of scientific questions, and
I should think that such a man ought to be the very best teacher
for young engineers.

Believe me to be yours most truly,

DR. H. HELMHOLTZ.
To Sir William Thomson, Glasgow!'

"UNIVERSITY OF EDINBURGH.
7 January 1873.

MY DEAR THOMSON,

I am very glad to hear that your brother is a Candidate
for the Chair of Engineering at Glasgow.

I was for some time his colleague in Belfast, and I can thus
state of my own knowledge that he is an excellent teacher, and
works in thorough harmony with his brother Professors.

As an original discoverer in Physics, and especially in the
Dynamical Theory of Heat, he holds a very high place indeed.
There are but few discoveries of the last fifty years which make
such a mark in the history of science as that of the lowering of the
freezing-point by pressure : for it has led, not only to numerous
kindred discoveries in pure science, but to the true physical theory
of glacier motion.

He has made many valuable contributions to Engineering,
among which I would specially mention his Turbine and his
Vortex Pumps, as being admirably based on true physical principles,
and thoroughly successful in practice.

I certainly do not believe that there can be found in Britain
any one so well qualified as he is to fill the place of our lamented
friend Rankine.

Yours ever,
P. G. TAIT."

"343 LOWER BRAUGHTON ROAD,
MANCHESTER.

7/1/1873.

DEAR THOMSON,

I wrote a testimonial for Mr two or three

days ago but when I did so I had no idea that your brother would
be able to leave Belfast. In the event of his seeking the Chair
of Glasgow College, it is impossible there can be any serious
competition, inasmuch as your brother's European fame as a

HIS GLASGOW COLLEAGUES Ixix

discoverer combined with his eminent success as a teacher of
Engineering science, are such as must place him altogether without
a rival.

Yours most truly,

JAMES P. JOULE."

"Jan. 7, 1873.

MY DEAR SIR WILLIAM,

I hope the enclosed will meet your views. As you
desired me to be very brief, I have avoided all details. Your
brother will indeed be a sad loss to us all here — and to no one
more than to myself. I have long been greatly attached to him,
and his departure will be a sad blank to me. He is indeed a rare
character, so truthful and gentle and wise withal... T. A."

The candidature was successful, and Prof, and Mrs Thomson
spent the Easter holidays in Glasgow on a visit to Sir William.
On the 17th April he was inducted to the Chair of Engineering,
and he commenced his duties in the following November.

The professors at the University at that time were an excep-
tionally interesting and genial set of men, and the social life of
the College was delightful. There was Principal Caird (an old
classfellow of student days)*, perhaps the greatest preacher in
Scotland of his generation, and certainly the most genial Principal
the University had had ; Dr Dickson, Professor of Divinity, with
his marvellous knowledge of apparently all the books in the College
library; Hugh Blackburn, Professor of Mathematics, learned, gentle
and retiring, and his charming wife, vivacious and accomplished,
who could draw, from memory, any scene she had witnessed;
Lushington, Tennyson's brother-in-law, was in the Greek Chair;
George Ramsay, a nephew of Thomson's old professor, held the
Chair of Latin; Duncan Weir, another old classfellow, was Professor
of Hebrew ; and the Principal's brother, Edward Caird, afterwards
Master of Balliol College, Oxford, was Professor of Moral Philosophy.

* In the Logic Class Session 1837 — 8 the following is the list of Prizemen in
the junior division:

1. Robert Douglas Kilbarchan (see pp. xxxvii, xxxix)

2. William Thomson Glasgow College

3. James Thomson Glasgow College

4. William Ker Glasgow (see pp. xxxix, Ixxxvii)

5. Claud Marshall Greenock

6. John Caird Greenock

7. Henry D. Taylor Dumfries

8. Peter MacFarlane Paisley

Ixx BIOGRAPHICAL SKETCH

All these lived in the Professors' Court in the dwelling houses
attached to their respective chairs. Then there was the genial
and enthusiastic Dr Grant, Professor of Astronomy, residing at
the Observatory, where he was ever ready and willing to devote
time and effort to showing the stars through the great telescope
to any of his colleagues, or even to the youngest members of their
families; and John Nichol, Professor of English Literature, was
eager to renew acquaintance with the friend of his youth, and
took pleasure in relating reminiscences of early days to James
Thomson's children. There was Sir James Roberton, one of the
law professors, a most charming conversationalist with endless
information about people and events of Scottish history ; * also
Robert Berry, afterwards Sheriff of Lanarkshire ; Sir George
McLeod, Professor of Surgery, tall and handsome, a brother of
the celebrated preacher Norman McLeod, who had died shortly
before ; Allen Thomson, Professor of Anatomy, to whose exertions
the success of the new University buildings was largely due; and
many others.

The old somewhat narrow spirit with regard to affairs of
religion had vanished ; Principal Caird's sermons were not only
eloquent, and full of deep thought and earnest feeling, but they
inculcated a broad toleration. At the time of James Thomson's
appointment to the Engineering professorship in Glasgow, his
brother William was still a widower; but in the summer of 1874
he sailed to Madeira in his yacht the Lalla Rookh, and there
married Frances Anna, daughter of Charles R. Blandy. Her
home-coming brought new brightness to the College Court, and
Sir William's lonely house was once more filled with cheerful
company.

James Thomson's introductory lecture to the Engineering Class
was a paper on Safety and Danger in Structures (No. 53, p. 349),
urging the importance of more frequent and more consistent
application of force tests. This subject had been before his mind
for many years. It was suggested to him by Professor Lewis D. B.
Gordon, who wrote to him on the 13th April 1862 : " I wish you
would write a neat paper on the principles which should decide
the coefficients of safety to be used in the application of materials
in construction. There is great confusion and error abroad on the
subject." His attention being thus directed he read a paper on
" Strength, Safety and Danger in Structures, with reference to

SCIENTIFIC WORK AT GLASGOW Ixxi

Amendment of Prevailing Practices " before the Belfast Literary
Society in 1867. This paper is not reprinted here. A paper on
" Comparison of Similar Structures as to Elasticity, Strength and
Stability " was read before the Institution of Engineers and Ship-
builders in Scotland on the 21st December 1875 (No. 54, p. 361).
Professor Archibald Barr has since extended and developed this
line of thought in his paper on " Similar Structures " read before
the same institution on 21st March 1899.

Early in 1874 Prof. James Thomson was asked to give the
James Watt lecture to the Philosophical Society at Greenock, and
selected for his subject "The Gaseous, Liquid, and Solid States of
Matter." The report of this lecture elicited the following letters
from Dr Andrews.

"QUEEN'S COLL., BELFAST, 5th Feb. 1874.
MY DEAK THOMSON,

I have received yours of the 28th and also the Glasgow
Herald containing a notice of your Watt Lecture. I am glad that
the experiments were successful, and that Bottomley was also able
to show the liquefaction of carbonic acid to the Nat. Phil. Class.
There is only one point on which I am afraid I should remonstrate.
You seem in your kindness to have given my poor work a little
too much prominence. However we are all vain and unprofitable
servants (I have been reading lately ' Old Mortality ') and bear a
good deal of flattery.

I was confined for 10 days to bed with this rheumatic attack,
but I am now nearly as brisk as ever. On the whole it was a
luxurious illness.

Cumine*, poor fellow, lost his wife about 6 weeks ago, and
attended her so faithfully that he brought on so serious an attack
of his bronchitic disease as seriously to endanger his life. He has
an order from Edinburgh for two of my compression apparatus, and
I expect he will soon execute your brother's order as well as it.
We have had an uninterrupted succession here of the finest weather
since Novr. To-day is magnificent and the noise of the elections
(if any) has not reached us. I was glad to see that Mr Gordon
has been returned again by Glasgow and Aberdeen. Home Rule
has been absolutely repudiated everywhere in Ulster.

Ever yours,

THOMAS ANDREWS.
P.S. Bessy and I are hard at work on Diderik van der Waals!"

* The mechanician who constructed Dr Andrews' apparatus.

Ixxii BIOGRAPHICAL SKETCH

The fundamental memoir of Johannes Diderik van der Waals
— a Leyden degree dissertation — published under the title Over
de continuiteit van den gasen vloeistoftoestand, Academisch proef-
schrift (Leiden : A. W. Sijthoff, 1873) — reduced the Andrews-
Thomson diagram to analytical form, by giving for the system of
curves an equation which applied over the whole range of the
gaseous and liquid states. The thermodynamic content of the
diagram thus became matter of quantitative deduction. The
earliest important public notice of this work was an elaborate
and appreciative, but withal critical, review by Clerk Maxwell
in Nature (Vol. x., pp. 477—480, Oct. 15, 1874), reprinted in his
Collected Papers, Vol. II., pp. 407 — 415. The subject *is also
touched by Clerk Maxwell in the lecture to the Chemical Society,
Feb. 18, 1875, "On the Dynamical Evidence of the Molecular
Constitution of Bodies " (Nature, Vol. XL, p. 359), where, after
referring to the exceedingly ingenious thesis of van der Waals,
since amply verified, he proceeds " his final result is certainly not
a complete expression for the interaction of real molecules, but his
attack on this difficult question is so able and so brave, that it
cannot fail to give a notable impulse to molecular Science. It has
certainly directed the attention of more than one inquirer to the
Low Dutch language in which it is written." As regards the
phenomena of mixed gases, on which so much progress has more
recently been made by the Dutch school, cf. also letters from
Clerk Maxwell to Andrews in the Scientific Papers of Thomas
Andrews, p. liv.

The following letter relates to an apparent discrepancy with
theory :

"QUEEN'S COLL., BELFAST,

April 15, 1874.

MY DEAR THOMSON,

...It is strange that we both overlooked a chapter in
Regnault's large work on steam (Mem. de I'Acad. 26. p. 751 et seq.)
in which he investigated the tension of acetic acid both in the
liquid and solid forms ; and obtained the same result which I had
done with the solid, freed as well as possible by crystallization
from the liquid ; viz. a higher tension for the solid than the liquid.
But suspecting as I had done that a trace of liquid was still present
with the solid, he distilled his acetic acid from anhydrous phosphoric
acid, and with the new body he attained your result, a lower tension
for the solid. He found however that a little acetone was formed
at the same time, and concludes that the differences observed were

SCIENTIFIC ACTIVITIES Ixxiii

due to foreign matters. I think I could now arrange an experiment
which would give decisive results; but I must wait for a more
convenient season. In a recent No. of the Annales de Chimie
there is I observe a paper on the subject. I have only seen the
title. Let me have the apparatus, if you have an opportunity
before the middle of June or beginning of July.
With very kind regards to Mrs T. and all yours

Believe me to be ever yours,

T. ANDREWS."

"QUEEN'S COLLEGE, BELFAST,

16 April, 1874.

MY DEAR THOMSON,

. ..I am deep in the Dutch paper, and also fully occupied
with my own results which I believe will turn out more important
than I supposed. But I miss you sadly,

Ever yours,

T. ANDREWS."

In 1874 the British Association met at Belfast, Prof. James
Thomson returning as President of the Mechanical Section. He
and Mrs Thomson were on that occasion the guests of their old
friend Prof. George Fuller. A few weeks later the Social Science
Congress met in Glasgow ; and Prof. Thomson, who was living in
a pleasant, roomy, old-fashioned residence " Oakfield House " close
to the University, had the happiness of welcoming a number of
Irish friends and relations to his new home. About this period,
Sir William Thomson was engaged on the invention of integrating
machines for the purpose of predicting the tides and, as usual, he
talked the matter over with his brother James, who remarked
"I wonder if my disc, ball and cylinder apparatus would help
you." The drawings and descriptions of it were brought out
and considered, and a model was made; and the result was the
well known series of tide-calculating machines of Sir William
Thomson*. James read a paper entitled "On an Integrating
Machine having a new Kinematic Principle " before the Royal
Society in 1876, No. 64, p. 452. This mechanism which his
brother was thus able to turn to useful account in the harmonic
analysis of the tides had been designed many years before. In the
earliest form it had a wheel revolving edgeways on the disc instead

* See infra p. 452 ; also Thomson and Tait's Natural Philosophy, Part I. 1879,
Appendix B. especially see pp. iii. iv. v.

T. /

Ixxiv BIOGRAPHICAL SKETCH

of the ball ; but the edge of the wheel partly slipping and partly
rolling did not please him as a mechanical contrivance, and he
substituted the ball, which, touching as it does only one spot,
is free from any kind of slipping. In an old note-book there is
a sketch of the early form dated August 1845.

Sir William Thomson brought the subject of the initial con-
traction of free liquid jets, as they issue from the orifice, before
the Philosophical Society of Glasgow on 23rd February 1876, by
communicating a letter containing a theory, now well known, of
the vena contracta, which he had received from William Froude;
and he appended an interesting letter of Sir Isaac Newton
on the same subject, then recently published in the Cotes
Correspondence. This led James Thomson to go over the
ground with some extensions, and to communicate an interesting
note on the vena contracta to the same Society (No. 15, p. 88).

In June 1876 Prof, and Mrs Thomson went up to London
to see a special loan collection of scientific apparatus at South
Kensington Museum in which both brothers had numerous
exhibits ; among others the Disc, Ball and Cylinder Integrator,
and the model surface to illustrate Dr Andrews' experiments on
carbonic acid.

In the same year he read before the British Association a
paper on Metric Units of Force, Energy, and Power, larger than
those on the Centimetre-Gram-Second System, and suitable for
practical use, infra p. 372.

In 1878 he communicated a paper on Dimensional Equations
and on related nomenclature in Numerical Science, infra p. 375,
which aims at simplification and precision in the language of this
fundamental subject.

In 1876 he wrote a paper (No. 16, p. 96) on another subject
which he had been considering for several years, viz. the behaviour
of water in river beds. The explanation there given, why the
inner bank near which the velocity is greatest does not wear
away more than the outer one, had occurred to him in 1872.
The British Association was to meet, under the presidency of
his friend Dr Andrews, in September, and a few days before
the meeting commenced, it occurred to him to try the thing
experimentally, in order to confirm the theory he had published
in May. On his brother's lecture room table he constructed a
clay model of a river bend, and turned on the water ; and to his

SCIENTIFIC ACTIVITIES Ixxv

great satisfaction, he found that the particles at the bottom, sand
and rounded seeds of various sizes, were carried across to the inner
side of the bend exactly as he had said they would go, while little
streamers of thread attached to pins showed the direction of flow
at the surface of the water. A wooden model was made for the
Exhibition in Kelvingrove Museum which was prepared for the
British Association. He had intended to clear away the original
clay model after showing it to his brother, in order to leave the
lecture room table tidy for the use of Section A. But when
Sir William saw the experiment he insisted on keeping the clay
model as it was, in order to let members of the Association see
the experiment and hear the explanation from the author himself.
A short communication describing the experiments was sent after-
wards to the Royal Society. Later, on the suggestion of Prof.
Barr, the course of the stream lines was indicated by little specks
of aniline dye introduced so as to adhere to the bed of the channel
at various places. (See paper No. 18, p. 106.)

In 1877 James Thomson was elected a Fellow of the Royal
Society. The following year the honorary degree of LL.D. was
conferred on him by the University of Dublin ; he had enjoyed
the same honour in his own University of Glasgow since 1870.
He also received the D.Sc. degree from the Queen's University
in Ireland.

At the end of 1877 Graham Bell came to Glasgow, and caused
much interest by explaining and showing to a large audience
his wonderful invention of the telephone, of which Sir William
Thomson had shown a rough example in his Presidential address
to Section A of the British Association at the meeting in the
previous year above referred to. He dined with the Thomsons,
and he and the Professor had much interesting talk both about
the telephone and about the system of visible speech invented
for the use of the deaf by Bell's father, Melville Bell. Prof.
Thomson was particularly interested in this, as both he and his
father had been strong adherents of phonetic spelling from the
time Isaac Pitman had first introduced it into this country.

As has been stated above, James Thomson studied many
geological questions. Thus he minutely examined the jointed
prismatic structure of basalt as seen at the Giant's Causeway
in Ireland, and elsewhere; and he concluded that the older
theories for explaining this phenomenon were untenable. As

Ixxvi BIOGRAPHICAL SKETCH

early as the 12th September 1861 he advanced, in a letter to
Dr Neilson Hancock, the germ of his own theory, which, after
much study, he gradually matured. Papers on this subject were
read before the Belfast Natural History and Philosophical Society
on 26th November 1862, before the British Association in 1863,
and before the Belfast Naturalists' Field Club on 17th November
1869. None of these papers are reprinted here, as the whole
theory was summed up in the paper read before the Geological
Society of Glasgow on the 8th of March 1877 (No. 62, p. 422).
It explains the columnar structure as being the result of shrinking
and cracking of the material during solidification ; and it holds
that the cross joints are, in reality, circular conchoidal fractures
commencing in the centre of the column and flashing out towards
the circumference, and that the tendency to cross fracture arises
from the expansion of the outer parts of the columns through
chemical action caused by infiltration of water.

During the sixteen years of James Thomson's tenure of the
Glasgow Professorship, the six months' vacation not only left
leisure for scientific work and engineering business, but enabled
him to spend several months annually at one or another of the
beautiful places of summer resort on the Firth of Clyde, the
Kyles of Bute, or Loch Long. At several of these places the
traces of glacial markings are visible. He used to take great
pleasure in studying these, and in particular in observing every
indication which might show the direction of the motion of the
ice. The result is recorded in the paper " On Features in Glacial
Markings noticed on Sandstone Conglomerates at Skelmorlie and
Aberfoil," No. 61, p. 420.

As one might well imagine, Professor Purser's visits, whether
in the country or at Oakfield House, were always a great pleasure
to the Thomsons. The following extracts from some of his letters
speak for themselves of the affectionate regard with which the
younger man approached his older friend and cheered him to the
end.

"25^ June 1879.

RATHMINES CASTLE, DUBLIN.

Fred was greatly pleased to receive the warm congratulations
you all have sent him. The more so as he knew you were amongst
the few who appreciated the difficulties of his position and approved
of his action when seven years ago he was obliged to forfeit the

SCIENTIFIC ACTIVITIES Ixxvii

fellowship he had won *....! should like very well to go to the
B. Assn. meeting for a part of the time at any rate, and help to
support our friend [Dr Johnstone] Stoney in Sec. A....

I confess to a strong feeling of satisfaction that my last visit
to Oakfield House has not been without its fruit, when it has
so completely revolutionized the mind of Dr Thomson on the
subject of V— 1, that whereas on that occasion his attitude to-
wards the ' imaginaries ' was one of such derisive scepticism as
to express doubt about the well recognised truth of two circles
meeting in two imaginary points at infinity, now on the other
hand he affectionately adopts these imaginaries and they are
henceforth to be no longer ostracised but lovingly included in
that great family who are to rejoice in the name of numerics !
See Note to Thomson and Tait, new edition p. 389. ' Quod
facit per alium facit per se.'

Fred is rejoicing in the change of his ' rdle ' from an examinee
to an examiner, and has been busy the last few days examining
in the omne scibile as comes natural to a junior fellow."

" May 13, 1886. Professor Thomson devoting himself to the
serious study of Hegelianism is a phenomenon !"

The following extracts from letters from Mrs Thomson to
her daughter, Bessie, describe two cruises taken during the
summer of 1880, the first in the Lalla Rookh, the second with

Dr Young •(• in the Nyanza.

"Saturday, 3 July 1880. OBAN.

Went ashore after kettledrum J to post letters, then had a
beautiful drive to Dunstaffnage and on up Loch Etive, past
Connel Ferry where the Falls of Lora or Connel are seen when
the tide is ebbing. This current (or rapids) is caused by the
narrow exit to which the great extent of Loch Etive is confined,
and the large quantity of fresh water accumulated in it during
the flood tide, and partly due to a reef of rocks. It was blowing
quite a gale from the N.E., so we were glad to be at anchor in
Oban bay. There was a faint red gleam at sunset; it was cold
but we had tea on deck and turned in at 10.45.

* In 1879 Frederick Purser, afterwards Professor of Natural Philosophy in
Trinity College, was elected a Fellow of Trinity College, Dublin. He had won a
fellowship there seven years before, but at that time the religious tests enforced
at Trinity College formed a barrier to his making the necessary declaration
on accepting it, because he was a Moravian. Seeing that the doctrines of the
Moravian community differed but little from those of the Church of Ireland, some
of his friends had tried to persuade him to accept the tests; but he felt that such
a course would not be right and Thomson sympathised in his scruples.

t Dr Young of Kelly, the friend of David Livingstone, introduced the manufac-
ture of paraffin oil from shale in Scotland. Dr Angus Smith of Manchester and
the Rev. Dr Robertson of Irvine were also of the party.

± Afternoon tea.

Ixxviii BIOGRAPHICAL SKETCH

Sunday, a lovely bright windy day, clear sky and more sun-
shine than we have seen since the day at lona on 22 June.
Went to church at Oban and had a little walk before coming
on board. We hope to have a walk on Kerrera after kettledrum.
We start tomorrow for home and will go either outside Islay or
down the Sound between Islay and Jura as we find the weather
will permit ; any way we expect to be back in Largs by Tuesday
some time....

E. T."

" KYLE AKIN, SKYE. 5.45 P.M., Saturday 7 Aug.

Left Isle Ornsay a little after one today and sailed up the
Kyles with a bright sun and a clear sky but not much wind.
We got on nicely through Kyle Rhea and Loch Alsh and had
a pretty view of Loch Duach and Loch Long. We then entered
the narrows of Kyle Akin when the wind failed and the tide had
previously turned against us at a critical part just opposite the
lighthouse. We got a boat out to put her head round and had
to get out the anchor to hinder us going aground, so here we are
in Kyle Akin and as the tide won't turn for some hours I suppose
we are here for the night instead of getting on to Portree...."

" KYLE AKIN ; Sunday, 8 August 1880.

This has been a showery day with bright gleams of sunshine.
The scenery is very beautiful, mountain, island and sea. We in-
tended to go ashore to hear the Gaelic service in a mission church
here. (The regular church is at Broadford 8 miles away.) Dr
Robertson and Dr Smith were to go for the whole service, while
the rest of us intended going to hear the end of the Gaelic service
and stay for the English service, but there was no minister here
and no service. The Missionary had gone to assist at a Communion
service at Balmacara, so Dr Robertson was asked to preach ; and
they hailed us from the beach to come ashore which we did and
a congregation was got together about 54 individuals. Dr Robertson
gave a very^ interesting sermon or rhapsody, which though not
logical carried one on by the eloquence of the man and the
poetical declamation. It all lasted about an hour....

Dr Young poured some oil over the side of the yacht and we
watched the calm spot for a long distance and saw what we had
intended — the gulls taken in by this calm spot and come to it in
search of food."

In 1882 another move, the last in Thomson's life, was forced
on his family, as the site of Oakfield House was wanted for the
building of a church. Mrs Thomson was then suffering from a
weak heart, and the removal to 2 Florentine Gardens was con-
ducted with great difficulty. An extract from a letter from

SCOTTISH YACHTING EXCURSIONS Ixxix

Mrs Elizabeth King to Mrs Thomson recalls that period, and is
interesting as it gives. Ruskin's opinion of her daughter Elizabeth
King's skill in portrait painting. The next letter written a year
later gives a graphic picture, in her daughter Agnes' words, of the
heads of the Thomson household at that time.

"15 BLOMFIELD TERRACE, May 2, 1882.

I am heartily glad that the house affair is so pleasantly
settled and that you have got the house you liked the best of
all you saw. I wish you much happiness in it with all heavenly
blessings. You will have a little while to enjoy the garden of
Oakfield before you leave, for which I suppose you will not be
sorry; and then will come the confusion and fatigue of moving,
which certainly is not enjoyable, but when it is over it is very
pleasant to feel settled and in order —

I must tell you that Ruskin has been admiring greatly the
portrait of James. He went to the Dudley with Mr Murray of
the British Museum, a gentleman George knows, and in walking
along he paused and remarked that was an excellent picture, and
desired Mr M. to turn up the catalogue to see who did it."

"April 23, 1883.

...Agnes brings a pleasant report of you. She says that
though not quite so strong as usual, you are so bright that you
are the life of the house. The house she says is beautiful and
so comfortable. Uncle James she says is full of fun and always
making merry jokes. Altogether she has had a very happy time
— a time that she will look back to with pleasure all her life.
It is a possession for ever...."

An extract from a letter dated October 1, 1883, from Professor
Thomson to his wife alludes to the " Law of Inertia " on which he
was writing a paper, No. 57, p. 379.

"...We have been at the College with William and Fanny.
We intended to stay very short and to post letters at Wilson
St. Pillar before 10.50: but there arose so much to spe&k of
and to listen to that the time for posting went past.... William
says he approves of the view I had expressed to him as to
Cayley's non- Euclidian, or dreamland, space. He has tonight
quickly glanced at my last writings about the ' Laws of Motion,'
and so far. as brief time permitted consideration, he seems to
approve of my teaching as to the laws of motion, or what ]
designate as The Law of Inertia. We spoke a good deal about
Typhoid Fever organisms or germs &c.

Your loving husband, J. T."

Ixxx BIOGRAPHICAL SKETCH

In 1884 James Thomson was elected President of the Institution
of Engineers and Shipbuilders in Scotland. In his presidential
address he gave his views on the fundamental principles of the
kinetic branch of dynamics, a subject on which he had long felt
the need of improvement in our modes of thought. "Lately,"
he said, " I have been able, I think, to clear up some parts of
this subject a little, and I have within the present year submitted
papers upon it to the Royal Society of Edinburgh [see Nos. 57, 58,
pp. 379, 389] and my sayings to you this evening will include
some passages from those papers." At the end of the address
he reverted to the question of safety in engineering structures
and insisted once more on the importance of more frequent and
more consistent application of force tests, on which he seized
every opportunity to influence the practice of engineers. He
dealt with the same question in more detail the following year
when he was again President. These views he repeatedly ex-
pressed on public occasions, and insisted on in private conversations ;
at first they met with considerable opposition on the part of
practical engineers, but they gradually moulded public opinion
in the direction of more definite criteria of safety.

During the summer of this year (1885) James Thomson went
up to London to give evidence, along with his brother William, on
the Manchester Ship Canal Bill which was then before Parliament.
He stayed with his sister, Mrs David King, at 24, Hamilton
Terrace. Extracts from letters received by Mrs Thomson from
her husband, and from his sister, show how he passed the time
while there.

"24, HAMILTON TERRACE, July 16, 1885.

James is off to spend the evening in the House of Commons.
Mr Brown* he expects to introduce him. He asked me to write
as he had no time. This morning he was at Thames Street seeing
about a stove for the studio, and he thinks he has found a good
plan for it. He is very bright and happy looking, and he says he
thinks his eye is about well. There have been no 'commas or
tadpoles ' troubling him of late, only sometimes a little dimness.
He won't be going home for a few days, as he must have a little
play now that his work at the Committee is finished. He is to
take our telescope with him, I do not need it at all....

Your affecte. sister, E. K."

* Now Sir Alexander Hargreaves Brown.

YACHTING AT COWES WITH LORD KELVIN Ixxxi

" YACHT Lalla Rookh, R.Y.S., COWES, WEDNESDAY, 22?id July, 1885.

We came here yesterday afternoon from Portsmouth Harbour
having a very pleasant sail in the Solent.

We were at anchor off Cowes during the night. Along with
E. King I have been intending to go back to London to-day; and
then to return home to Scotland with as little delay in London as
possible. I have been feeling some incipient uneasiness on the
score of liability to accusations of wife and family desertion : as to
which I got some premonitory suggestions in Mary's letter of
Saturday last. Wm. has however this morning persuaded me
to stay till tomorrow (or possibly till Friday morning) so as to
continue the cruise to..."

"YACHT, Lalla Rookh. At anchor, COWES.

Thursday, 2Zrd July, 1885.

There are great festivities going on all round for the wedding
of the Princess Beatrice. The actual wedding ceremony is to be
today at 1 J p.m. or therabouts. The Prince of Wales' steam yacht
Osborne, and the Queen's steam yacht Victoria & Albert, are at
anchor very near us. The Prince of Wales has just gone ashore
in a small steam launch which we saw passing near us. Capt.
Fisher* who has been away in the evolutionary squadron round
the coasts of Ireland, has just arrived in the English Waters at
Spithead, and has come on here without any landing at Portsmouth.
Wm. spoke him as he was going ashore a few minutes ago to Cowes
to be at the wedding. Mrs Fisher and her three daughters have
now come on board the Lalla Rookh and are on deck. Miss Fisher
is much interested in drawing, which she has been learning at the
Gosport School of Artf. She is involved in the mysteries of
perspective examples, taught by rules mostly (Qy all ?) not under-
stood:— but I suppose knowledge is longed forj...."

About this time politics were attracting much attention. In
the winter of 1885 a ballon d'essai was sent up by Mr Herbert
Gladstone (now Viscount Gladstone) suggesting the adoption by
the Liberal Party of the policy of Home Rule. James Thomson
immediately perceived the danger impending and pointed ID out
very clearly to his friends. He used all his influence to oppose
the scheme, both then and later when it was adopted as the official

* Now Admiral of the Fleet Lord Fisher.

t Miss Fisher designed one of the supporters to Sir William Thomson's Coat of
Arms when he was raised to the peerage, and his niece Bessie Thomson designed
the other.

J Professor Thomson had always been much interested in perspective ; finding
the teaching in books on Art in his day very defective, he planned out a book on
the subject but unfortunately did not live to completed it.

Ixxxii BIOGRAPHICAL SKETCH

policy of the Liberal Party. It may be said that his and his
brother's influence was largely felt in Glasgow and the West of
Scotland, where the most powerful Liberals ranged themselves
with the Liberal Unionist Party then being formed by Lord
Hartington and Mr Chamberlain.

To Mrs Thomson.

"July 7, 1886. Wednesday, 5.45P.M.

I got to Glasgow all right yesterday. I posted the Post cards
at the General P.O. I dined here with Fanny. Wm. was gone
to a meeting at Johnstone. Then I went in haste to a meeting
of Craig Sellar's in the Burgh Hall, Partick. I have been out
with Wm. at a good many places before luncheon. Have* been
canvassing in Athole Gardens since. Everybody (almost) away
except in evenings and mornings. I am now hastening to the
Western Club to dine there with Mr Crichton in order to go
with him to a meeting in Borough Hall, Kinning Park, of
Mr Shaw Stewart's candidature for East Renfrewshire. It is
likely that I shall have to make a short speech, no more than
to second some motion. Mr Shaw Stewart is a moderate con-
servative, and I may do good as a decided liberal favouring him as
unionist. In haste.

J. T."

The next letters from Sir Wm. Thomson show how in their
scientific as in their political work the two brothers kept in close
touch to the end.

"Aug. 15/87.

NETHERHALL, LARGS, AYRSHIRE.
DEAR JAMES,

I have been under intense stress since you left us, till
yesterday morning when I got off a 3d & last instalment of a paper
for the Sept? Phil. Mag* on the stability of laminar motion of a
uniform broad river on a plane bottom ; and so have been prevented
from thanking you sooner for your two letters with enclosures all
of which came most opportunely and acceptably. I return the
Ice Abstract •(• which came before Stokes left, and we were both
much interested in it. It settles absolutely Tyndall's & Huxley's
contention against Forbes, and shows conclusively that there is
viscosity, even without your thermodynamic considerations. So
Forbes is now proved quite unqualifiedly to have been right.

I am now going on to the * turbulent ' motion of a river or of
water between two planes, & I am very glad to have your ' Uniform

* Math, and Phys. Papers, Vol. iv. p. 308.

f "Note on Some Experiments on the Viscosity of Ice" by J. F. Main, M.A.,
D.Sc., Proc. Royal Society, April 1887.

RESISTANCE OF FLOWING WATER Ixxxiii

Regime*/ I shall carefully keep both the printed articles, & return
them to you as soon as I have done with them, which I suppose
will be as soon as my paper is read at the B. A. in Manchester, or
as I have got the MSS. of it sent off to the Phil. Mag. which I hope
may be before the meeting. But now I want very much a practical
formula for the flow of water in as smooth a channel as may be.
Do you remember the coefficient of 'wetted perimeter' which
we used, in the investigation before the House of Commons
Committee on the Manchester Ship Canal ? If you have not it
by you I could easily get it by writing to Deacon. I want to
compare the actual flow with what it would be on the same slope
if the motion were laminar (rectilineal). Did I tell you that
I found Froude's resistance to a plane 50 feet long moved at
10 ft. (300 centimetres) per second through water in a wide deep
canal is the same as it would be if the fixed plane were 1/30 of
a centimetre from it, & the motion laminar? A corresponding
comparison as to the flow of a river will be most interesting &
important. . .

Your Affte brother

WILLIAM THOMSON."

"Aug. 18/87.

NETHERHALL, LARGS, AYRSHIRE.

DEAR JAMES,

I am greatly obliged to you for your ' Notes ' ! They
give me exactly & all what I want. I wanted the circular tube
also, and was going to ask you for it next, but you have happily
anticipated me.

Weissbach's formula for the tube agrees beautifully with
Osborne Reynolds' conclusion that resistance a F1'73 for velo-
cities above those fors which the flow is rectilineal, in a straight
tube of circular cross section. For, taking

we find

d(logF)

Hence when F = 1 foot per sec.,

d (log y) _ -. .,-ah. .
-

See infra, p. 106.

Ixxxiv BIOGRAPHICAL SKETCH

and through a wide range of velocities the difference of 7 ;. ° Trx

d (log F)

differs little from Osborne Reynolds' value T73. It increases from
1-5 when F= 0 to 2'0 when F= oo .

I had come to the conclusion that if resistance oc FM be
taken, as Reynolds (& Froude) took it, as an empirical formula,
n must probably increase towards, or to, 2, as F increases. The
mathematical theory of Turbulent Flow between two planes is
coming out beautifully, and I am almost sure now that it will
bring out your, and the observational, result, of maxm velocity at
some distance below the surface of a broad open (not ice-covered)
river flowing in uniform regime over a uniformly inclined plane
bed. I enclose a rough proof which you may burn*. Read, if you
care, the § 41 & the non-mathematical part of § 48 and § 49. *

Your affcte brother, W. T.

I am now at work on the ' Turbulent Flow ' for the B. A.
meeting & the Oct. number of the Phil. Mag.

Fanny joins me in love to all. It is a great comfort and
advantage to me to have your ' Notes/

P.S. — Osborne Reynolds founds entirely on Darcy & Bazin's
observations besides his own. He does not use their empirical
formula and uses their results very unclearly and unexplicitly.
Altogether although his paper is very important it is made quite
needlessly difficult. Do Eitelwein and Weissbach depend on Darcy
and Bazin ? "

Long previously a correspondence on the modulus of viscosity
of water, which may here be reproduced, had passed with a view
to preparation for Thomson and Tait's Natural Philosophy.

"GLASGOW, Feb. 19/62.
MY DEAR JAMES,

...I write now chiefly to ask you about the flow of
water or other fluids through pipes. The theoretical expression
I have just worked out, and I find it to be

h. the head of liquid. r. radius of tube.

Q = 2L — I- length. p. coeff fc measuring the viscosity.

Sfji ' I Q. the number of units of volume flowing per

second,

when the motion is so slow as to be steady, i.e. simple slipping in
parallel layers, without eddies or inequalities. I can easily send
you the proof if you please.

/JL denotes the tangential traction per unit area required to
keep a plane layer of fluid, of which one side is held fixed in such

* Math, and Phys. Papers, Sir W. Thomson, Vol. iv. pp. 330, 335.

FRICTIONAL FLOW IN PIPES Ixxxv

a state of regular internal sliding (i.e. continuous change of shape)
that portions of it at unit distance from the fixed plane shall
move at unit velocity. I call JJL simply 'the viscosity.' Stokes
derives its value for water from Coulomb's experiments on the
oscillations of discs under water, when influenced by the elastic
force of torsion. The rate of decrease of the arc of vibration is the
subject of measurement. When this comes to bear a constant
proportion to the amount of the arc at any time, the resistance
must be proportional to the velocity simply, & the motion must
be regular, free from eddies, and consisting of pure, steady, internal
slipping or continuous change of shape by motions in circles
parallel to the plane of the disc and having their centres in its
axis. But I suspect the effect of eddies and irregularities cannot
have been perfectly kept clear of, because the value of /u, deduced
by Stokes seems too great. It is '82 x 10~5 when 1 square inch
is the unit area and 1 inch head of water the unit pressure.
Substituted in the preceding formula, this gives

where D = 2r (the diameter of the tube). Now it appears that

Poiseuille by pure experiment arrived at the theoretical law - ;

d

and, reducing his formula to the units stated above I find it to be

/?/)4
Q = 3400 (1 + -03368* + -00022U2)-^- .

i

This is 10 per cent, too great a discharge for Stokes's //, to
allow, even at temperature 0° Cent. At 10° or 15°, the probable
temperature of Coulomb's experiments, the discrepance would be
considerably greater, as Poiseuille's result indicates a rapidly
decreasing viscosity as temperature rises.

G. Hagen arrives at very nearly the same result, so far as the
cases in which his tubes were long enough. His value at freezing
for Q, is just 1 per cent, less than Poiseuille's. A little above
0° Cent, it will agree perfectly, and still higher it will be somewhat
larger than Poiseuille's. This seems to confirm P.'s result and to
show that Coulomb's gives too great viscosity.

On the other hand, Stokes finds that Dubuat's observations
on the times of vibration of pendulums oscillating under water
lead to considerably smaller value of JJL than Coulomb's, and
I daresay may agree with Poiseuille's. But Bessel's results on
pendulums agree very closely in the //, Stokes finds from them,
with Coulomb's ; and hence I suppose it was that Stokes preferred
Coulomb. I want to give good information on this in the Book
(Tait and Thomson's elements of Natural Philosophy) and I should

Ixxxvi BIOGRAPHICAL SKETCH

be much obliged by any information you can give me ; including
the formulae you use and consider best.

Your aff te brother W. T."

From William Thomson to James Thomson.

"Feb. 25/62.

I have looked up Helmholtz's paper since I wrote last; and
I have no doubt that he is right that there is finite slipping of
water over some solids, for instance, polished gold or silver. H.'s
experiments are of a most unobjectionable character — the time of
oscillation and the decrease of arc of a hollow globe filled with
water, and made to oscillate by torsion or bifilar suspensions about
a vertical diameter — the time of vibration was about 24 seconds.
The decrease of the arc was in perfectly constant proportion, which
proves the resistance of viscosity to have been simply as the
velocity and no disturbance to have taken place from eddies or
other irregular motions."

A Post Card.

"NETHERHALL,
Sunday morning, Aug. 28, 1887.

Many thanks for copy of statement regarding 'viscosity of
metals*' which is very clear and satisfactory. Remember me
kindly to Pursers, and tell them the turbulent flow (rivers) ques-
tion has led me to a solution for propagation of laminar motion
through an infinite turbul entry moving inviscid liquid (the magni-
tude of orbits and other dimensions of the turbulent motions
exceedingly small) which gives velocity of propagation of a plane
wave (as of light in the luminiferous ether) = i \/2 of mean velocity
Vmean square of the turbulent motions. This seems almost to
establish the vortex theory for the constitution of the interstellar
ether. W. T."

In 1888 when Prof, and Mrs Thomson were staying at Coul-
port on Loch Long, her brother Dr Neilson Hancock and his wife
came over from Ireland to spend the summer with them. The
two men had been friends before they became related to each
other by marriage, and there had always been a close bond of
union between them. A few days after their arrival on a beautiful
evening in July, Dr Hancock was seized with angina pectoris, and
in twenty minutes he was dead. Thus was sadden gloom cast
over the home that had been so full of happiness. Their children

* See infra, p. 406.

FAILURE OF HIS SIGHT Ixxxvii

noticed that after this, both Prof, and Mrs Thomson began to feel
their years. Still, the same patient spirit which had tided them
through earlier sorrows and anxieties did not fail them now, and
their gentle resignation was a lifelong lesson to the younger
members of the family.

Prof. Thomson continued the lectures to his classes during
the succeeding winter. He contributed a paper to the British
Association on "Flux and Reflux" (No. 20, p. 123), his last
published work on the motion of water in rivers.

The following summer was spent at Toward Point, the
widowed sister-in-law being one of the family party. In the
autumn, shortly before the time for returning to Glasgow, a new
calamity befel Prof. Thomson, the failure of his sight. The
retina became detached in the middle, with the result that in
a few days he could no longer see to read and could only write
with difficulty, because the part of the page before him directly in
the middle of the field of view seemed always to disappear, or to
become so distorted, that the words written on the paper could
not be distinguished. Happily total blindness never came on;
even to the end of his life he could see light and colours and could
to a certain extent recognize the faces of friends. When he be-
came more used to the deprivation of clear sight, he learned to
write with a blunt black pencil on large sheets of cartridge paper,
or better still, with chalk on a large slate, for his wife or one of
his daughters to copy. Dictating always seemed to be difficult to
him. By the aid of a magnifying glass and by directing his eyes
a little above or below the thing he wanted to examine, he con-
trived sometimes to study a diagram or a formula which thus had
its image on an uninjured part of the retina. The immediate
result of his failure of sight was that he felt obliged to resign his
professorship. Under this affliction his wonderful patience again
asserted itself. He never complained nor was the sweetness of
his disposition ruffled in the slightest degree. He still employed
his mind with scientific work, even under all the inevitable dis-
advantages, and took relaxation in listening to the reading aloud
of literature, and continued his interest in politics. The visits of
his brother and of the friend of his youth Mr William Ker, who
came to see him almost daily and walked out with him, were a
great source of pleasure. There was also much happy intercourse
with Prof. William Jack and others among his former colleagues,

Ixxxviii BIOGRAPHICAL SKETCH

who managed even in the midst of the strenuous work of the
College session to find time to come frequently to see him.

It was a source of great gratification to him when his former
assistant Prof. Archibald Barr was appointed as his successor in
the Engineering chair. Prof. Barr had been one of his students,
and has taken many opportunities to express appreciation of his
teaching ; the following is from a letter written to Mrs Thomson
just after his appointment as Professor of Engineering at Leeds,
in 1884.

"I have taken this opportunity of writing to you, because
I cannot allow myself to settle down to my new work without
expressing to you my sense of the great kindness shown to me by
yourself and family during the past eight years.

I can assure you that your kindness has been much felt by
me, and will always be gratefully remembered.

It will be needless for me to say how much I am indebted to
Professor Thomson. If I am in any way fit for my present position
I owe it — I need hardly say — to him. I took the opportunity
offered by my opening evening lecture to acknowledge somewhat
publicly in Leeds how much of my knowledge of Engineering
Science I owe to Prof. Thomson. I find it difficult to make any
statement of a fact or a principle to my classes without echoing
what I have learned from him, proving that I am one of the many
echoes of which Goethe speaks in the quotation which I made use
of in my lecture. I can only hope that I may be a faithful echo,
of which there are, I fear, very few*...."

Prof. Thomson continued to take a great interest in the welfare
of the Engineering department. He had some correspondence
with his old colleague Prof. Purser on the subject of how practical
work might be combined with the theoretical teaching of engineer-
ing. Prof. Purser has written as follows :

"QUEEN'S COLLEGE, BELFAST,

2 Dec., 1889.

In Medicine the students learn theory and practice simul-
taneously, walk the hospitals while they are attending lectures.
It would appear very desirable that they should follow a similar
plan in Engineering. FitzGeraldf tells me there would be great
difficulties in this, that in places like Harland and Wolff's or
Combe and Barbour's young men who did not give them their

* " There are many echoes in the world, but few voices." GOETHE.
t Prof. Maurice FitzGerald, George Fuller's successor in the Engineering
Class at Belfast.

RESIGNATION OF PROFESSORSHIP Ixxxix

whole time would be very much in the way, and would idle the
other pupils, and that any plan for practical millwright work in
College would be very costly."

On the llth December, 1889, a dinner was given in honour of
James Thomson and two of his colleagues, John Nichol and Richard
(afterwards Sir Richard) Jebb, who were all three resigning their
chairs in Glasgow University, the last named having been
appointed Public Orator in his own University of Cambridge.

Mr James A. Campbell, M.P. for the University, in the course
of his speech said :

" I have now the honour to propose the toast of the evening —
'Our Guests.' We are assembled to-night to do honour to three
distinguished gentlemen who have lately retired from the position
of professors in our University. For many years past they have
exercised the function of professors with great credit to themselves
and signal advantage and honour to the University. And now
that they have demitted office — two of them, I regret to say,
because they were no longer feeling equal to the strain of its
duties — it becomes us to take the opportunity of acknowledging
our gratitude to them, for we know what their services have been
— not only our gratitude, but the gratitude of many others who
sympathise with us — and also to wish them health and happiness
in the future...."

Principal Caird in responding at the close of the dinner said :

" * * * The resignation of a professor is not always an unmiti-
gated misfortune to a University. It is hard indeed for any man
to believe that his best days are over — to let the conviction dawn
on his mind, for instance, that the same old lectures that have so
often done good service in the past are a commodity that by long
exposure to the air has lost much of its original pungency. Yet
though it is not in nature that a man himself should find consola-
tion for retirement from office in the thought of lessened efficiency,
other people may. Need I say that on the present occasion no
such consolation can be ours ? In the case of Dr James Thomson
our regret for his retirement is indeed deepened by the fact that
it is due, as its immediate cause, to a serious, but we all hope, only
'temporary physical ailment. That it is not due to any abatement
of intellectual activity, of scientific interest or ingenuity, or of
delight in expounding to others the results of his thought and
research, any one, who, like myself, has visited and conversed with
him since his retirement, can bear confident witness....

But gentlemen, let me say in conclusion it is not in his
writings, however excellent, that the best memorial of a great
teacher is to be found. We can perhaps recall the names of

T. a

XC BIOGRAPHICAL SKETCH

honoured teachers who, whether from lack of literary ambition or of
productive activity of mind, have done little to enrich the literature
of their subject. But be their books many or few, it is not in these
that the teachers whom we revere and honour, and on the thought
of whom we love to linger, have left in our minds the deepest im-
pression of their powers. By their mastery of their subject and
their power of awakening something of their own love for it in other
and younger minds, by their marvellous skill in the art of communi-
cating knowledge, their forbearance with the dull, and stimulating
sympathy with the bright and clever, by their patient and un-
grudging expenditure of time and labour on our behalf, and above
all, by the impulse derived from daily contact with the personality
of a great teacher, — by these and similar means they have created
for themselves in the intellectual and moral life of their pupils
a memorial better and more precious than books, graven, while
memory lasts, in the living tablet of human hearts and minds."

For nearly three years after his resignation Dr Thomson lived
happily and quietly. He now found time to complete his work on
a subject which had been long before his mind, i.e. the theory of
the grand currents of the atmospheric circulation. His first paper
on this subject had been read at the British Association in 1857
(No. 26); another one given to the Belfast Natural History and
Philosophical Society on 6th April, 1859, was similar in terms and
has been omitted here. Later on, the same topic formed the
subject of the "James Watt Lecture" delivered before the Philo-
sophical Society of Greenock on 15th January, 1886. The paper
on Whirlwinds and Waterspouts read at the British Association
in 1884 (No. 27, p. 148), treats of a part of the same general
theme. In his opinion the diminished pressure in the centre of a
whirlwind is the cause rather than the effect of the rapid whirling
motion, as against the view of other writers on this subject that
the diminished pressure was due to the gyratory motion of the air.
He urged the encouragement of accurate observation, and the
collection and scrutiny of observed facts and appearances, as a
foundation for careful theoretical consideration. The last paper
he wrote, when his eyesight was nearly gone, was a recapitulation
of all his work on Atmospheric Circulation ; this valuable Memoir
(No. 28, p. 153), obtained the distinction of being chosen to be the
Bakerian Lecture of the Royal Society for 1892, and was read on
the 10th March of that year by his brother, then President of
the Society. The following extracts from two letters received
from Prof. John Purser show a sympathetic interest in the work.

FINAL YEARS xci

"Feb. 10, 1891.

I am very glad to learn that you are taking up again your
old work on Atmospheric Circulation, and that you are proposing
to put together what you have written and what you may now
add in a new paper. I think I discern your brother's direction
turning your thoughts towards this subject."

"RATHMINES, DUBLIN,

26 Dec, 1891.

I am much interested to hear that the paper on Atmosph.
Circn. is going forward and that this enquiry is leading to these
others about the phenomena connected with the rotation on their
axes of the Sun and Jupiter."

Barely two months after the Bakerian Lecture, on May 8th,
1892, he passed away, his active and courageous mind still in
pursuit of knowledge. Within a week his youngest daughter
Bessie and his beloved and devoted wife followed him.

A most fitting close to this sketch is afforded by the words of
Principal Caird in conclusion of his opening sermon to the
University of Glasgow in November, 1892. They allude to the
three Professors who had died in that year, Sir George McLeod,
Dr Grant, and Professor James Thomson.

"I have no intention to-day to lay the individual character
and career of each before you, further than to say in a single
sentence that they were one and all men of no little grade in
scientific attainment and of most enthusiastic devotion each to his
special department, whether as teachers or as original enquirers.
All of them were men of pure and lofty character, who drew to
themselves the admiration and respect of all connected with them,
whether as colleagues or pupils. We, who have been for long
years associated with them in this place, can never cease to cherish
their memory. They were devoted to noble ends, and of untiring,
unflagging application, and pure and blameless lives. Can such
lives be for ever lost to the world ? Are they, and such as they,
given to God's Universe only as shadows appearing for a little and
then vanishing for ever away ? Has all this lofty intelligence
been created only for a few short years of a life — short at the
longest — and then to be flung recklessly away ? Can we hold our
belief in God after such a thought ? Do you believe it ? When
I can believe that man is more wise and merciful than God, and
human thought more trustworthy than divine, then, and not till
then, will I believe that He spake falsely, who declared ' I give
unto them eternal life, and they shall never perish.'"

xcii OBITUARY NOTICE

OBITUARY NOTICE BY DR J. T. BOTTOMLEY, F.R.S.

[From the Proceedings of the Royal Society, Vol. LIU. 1893.]

JAMES THOMSON, lately Professor of Civil Engineering and
Mechanics in the University of Glasgow, was born in Belfast on
February 16, 1822.

His father, a mathematician of very high order, was, in the first
instance, Mathematical Master and Professor of Mathematics in the
Royal Belfast Academical Institution; but in 1832 became Professor
of Mathematics in Glasgow University.

James Thomson, and his brother William, Lord Kelvin, entered
the classes at Glasgow University at an unusually early age. They
were never at school, having received their early education at home
from their father. They passed through the University together,
both with high distinction, the two lads usually obtaining the first
and second prizes in each of the classes they attended.

At a very early age also James Thomson showed evidence of
considerable inventive genius. When he was about sixteen or
seventeen he invented a mechanism for feathering the floats of
the paddles of paddle steamers. Steamboats, even on the Clyde,
were comparatively novel in those days; and the invention was
looked on with much interest by the Clyde engineers to whom it
was shown. Unfortunately, from a commercial point of view, how-
ever, it turned out that another method of accomplishing the same
object had been invented and patented only a few months earlier.

After passing through the University curriculum, James
Thomson took the degree of M.A. with honours in Mathematics
and Natural Philosophy at the age of seventeen [eighteen].

As he had decided on adopting civil engineering as his pro-
fession, he went, in the autumn of 1840, to the office of Mr Macneill
(afterwards Sir John Macneill), in Dublin. But unfortunately his
health had, shortly before, to some extent, broken down. He was
obliged to leave Mr Macneill's office after about three weeks and
return home.

In 1840 a new departure was made in Glasgow University,
which proved of great importance, and which has had far-reaching

BY DR J. T. BOTTOMLEY xciii

influence on the practical teaching of engineering in this country.
This was the foundation, by Queen Victoria, of the first Chair of
Civil Engineering and Mechanics in the United Kingdom. The
first professor was Lewis Gordon, who was succeeded fifteen years
later by Macquorn Rankine. James Thomson, at home and in
delicate health, attended Professor Gordon's classes in engineering,
and was busy with inventions of various sorts; and particularly
with a curious boat, which, by means of paddles and legs reaching
to the bottom, was able to propel itself up a river, walking against
the stream.

In 1843 he was able to resume work as an engineer, and he
went to Millwall, to the works of Messrs Fairbairn and Co., of
London and Manchester. He was not, however, able to remain
with them for the full time of his apprenticeship. Illness re-
turned; he was obliged to go home; and this illness proved the
commencement of a period of delicate health which lasted for
years, and, indeed, produced a permanent effect on his whole life.

During the months which he spent at Millwall, he was busy
with improvements in furnace construction for the purpose of
prevention of smoke. The gases of combustion were to be taken
downwards through the furnace instead of upwards ; and the fire
bars were to be tubes with water circulating through them.

After his return to Glasgow he was obliged to confine himself
to work which did not involve bodily fatigue. He occupied him-
self much with invention ; and particularly gave his attention to
machines for the utilisation of water power.

He constructed a horizontal water-wheel, which he named a
Danaide, being an improvement on the Danaide of Manouri
d'Ecfcot; and somewhat later, after much investigation and re-
search, he invented a wheel which, from the nature of its action,
he called the vortex water-wheel. This form of wheel was patented
in 1850. It was an important advance on water-wheels of previous
construction. The moving wheel was mounted within a chamber
of nearly circular form. The water, injected under pressure, was
directed, by guide blades, to flow tangentially to the circumference
of the wheel ; and was led through the wheel to the centre by
suitably formed radiating partitions. Thus the water yielded its
kinetic energy derived from one half of the fall, and its potential
energy from the other half, to the wheel by pressure on the radial
partitions, as it passed inwards to the centre, whence it quietly

XC1V OBITUARY NOTICE

flowed away in the tail-race. A considerable number of these
wheels were designed by him for various factories and for different
purposes. They were made and supplied by Messrs Williamson
Bros., of Kendal, and gave much satisfaction.

In 1847 his mind was also busy with a question to which at a
later date he gave much thought and labour, and to the solution
of which he made contributions of great importance. On April 5
of this year there appears a memorandum in his handwriting: —
"This morning I found the explanation of the slow motion of
semi-fluid masses such as glaciers."

During 1848 his first three important scientific papers were
published. The first of these was on " Strength of Materials as
influenced by the existence or non-existence of certain mutual
Strains among the Particles composing them." The second was
a remarkable paper on "The Elasticity and Strength of Spiral
Springs and of Bars subjected to Torsion." In this paper the
action of a spiral spring was explained, and important principles
connected with the subject of torsion were brought forward.
These papers were published in the Cambridge and Dublin Mathe-
matical Journal, November, 1848.

The third was, perhaps, yet more remarkable. It was con-
tributed to the Royal Society of Edinburgh, and was on " The
Parallel Roads or Terraces of Lochaber (Glenroy)." These remark-
able terraces or shelves had attracted much attention. Darwin,
Lyell, David Milne, Sir G. Mackenzie, Agassiz, Sir Thomas Dick
Lauder, and others had discussed the causes of their formation.
James Thomson, however, gave in this paper what is now the
accepted explanation.

Curiously, Professor Tyndall seems not even to have known of
the existence of the paper when he gave his admirable exposition
of this wonderful natural formation at the Royal Institution in
1876. He attributes the explanation of the Parallel Roads to
Jamieson, 1863 ; whereas the whole theory had been given by
Thomson in 1848 in the paper just mentioned, with details as to
necessary climatic circumstances not noticed by Tyndall.

In January, 1849, he communicated to the Royal Society of
Edinburgh a paper of great importance, which was printed in the
Transactions of the Society, and was afterwards republished, with
some slight alterations by the author, in the Cambridge and
Dublin Mathematical Journal, November, 1850. The title of this

BY DR J. T. BOTTOMLEY XCV

paper was "Theoretical Considerations on the Effect of Pressure
in lowering the Freezing Point of Water." The principles ex-
pounded in this paper were afterwards, in 1857, used as the
foundation of his wellknown explanation of the plasticity of ice,
discovered by Forbes; and later, from 1857 onwards, for several
years, the whole subject afforded him much food for thought ; and
extensions and developments in various directions followed. The
paper of 1849 was of great intrinsic importance. In it, by the
application of Carnot's principle, an absolutely unsuspected physi-
cal phenomenon was discovered and predicted, and the amount
of lowering of the freezing point of water was calculated. The
phenomenon was shortly after experimentally tested and confirmed
by his brother, Lord Kelvin.

But the paper has another title to interest, which is not so
generally known. In it [as reprinted in November, 1850, by
means of an alteration in one sentence] for the first time Carnot's
principle was stated, and Carnot's cycle described, in words care-
fully chosen, so as not to involve the assumption of the material
theory of heat, or rather, as Thomson himself puts it, the suppo-
sition of the " perfect conservation of heat."

For the sake of clearness, it may be well to leave here for a
moment the chronological order of James Thomson's life, and to
explain briefly the subsequent development of the ideas first
disclosed in this paper of 1849.

Forbes had discovered, by observations and experiments on
the Swiss glaciers, the property of plasticity in ice. The fact of
plasticity in ice was at first doubted ; but it was afterwards
admitted, and various explanations were offered of this property,
so remarkable in a brittle and, above all, crystalline substance.

In this connection, Faraday called attention to the freezing
together of two pieces of ice placed together in water ; and from
this arose a partial explanation, by Tyndall, under the designation
of " Fracture and Regelation." But the theory, and even the not
logical juxtaposition of the two words, did not satisfy James
Thomson. There was nothing to show why or how reunion (or
" regelation ") should take place after fracture. He saw, however,
that an extension of his own previous principle of lowering of the
freezing point by pressure allowed him to apply it to the effect of
distorting stress on solid ice, and would give a perfect explanation
of all Faraday's observations and experiments on the union and

XCV1 OBITUARY NOTICE

growth of the connecting link between two pieces of ice under
water, pressed together by any force, however small.

By this extended thermodynamic principle he also accounted
for the yielding of a mass of ice crystals (dry snow, for instance)
at temperatures lower than the ordinary freezing point. He demon-
strated that the mutual pressures must melt the ice at, and close
around, the points of contact ; and that, when there is relief from
the internal stress by this melting, the low temperature of the
main solid mass, and the extra cold due to the latent heat required
for liquefaction of the yielding portions, cause the melted matter
to re-freeze in the places to which it has escaped in order to
relieve itself from strain. Thus a complete explanation, based on
a demonstrated physical principle, was offered of the phenomenon.

Thomson's explanation did not, certainly at first, commend
itself thoroughly to Faraday. A very interesting correspondence
between them ensued ; and Faraday made a number of beautiful
and interesting experiments, with the object of showing that the
placing of two pieces of ice on opposite sides of a film of water
(between them) would give rise to the conversion of the film of
water into ice, and cause the union of the two pieces of ice, the
principle being that of the starting of crystallisation in a super-
saturated solution by means of a crystal of the solid. James
Thomson, however, showed that, in the experiments adduced by
Faraday, pressure between the ice blocks was not absent. For
example, in an experiment in which two pieces of ice, with a hole
through each, were mounted on a horizontal rod of glass, he
pointed out that the capillary film of water between the slabs
draws them together with not inconsiderable mutual pressure,
and hence the freezing. Thomson further showed that when two
pieces of ice are brought to touch each other at a point wholly
immersed under water, and thus free from capillary action, the
most minute pressure pushing the two together causes the growth
of a narrow connecting neck, which may be made to grow by con-
tinued application of the pressure ; while the application of the
smallest force tending to draw the two asunder causes the neck to
diminish in thickness, and finally to disappear.

In later years James Thomson further developed the theory of
1849. He showed that stresses, of other kinds than pressure
equal in all directions, can relieve themselves by means of local
lowering of the freezing point in ice-; and he showed, by theory

BY DR J. T. BOTTOMLEY XCV11

and by experiment, that the application of stresses may assist or
hinder the growth of crystals in saturated solutions. Some of
these conclusions are of such importance that they deserve to be
better known. The title of the paper in which the last-named
results were given is, " On Crystallisation and Liquefaction as
Influenced by Stresses tending to Change of Form in the Crystals*,"
1861. It included the amended and extended theory of the plas-
ticity of ice.

In 1850, James Thomson was engaged in perfecting his design
for the Vortex water-wheel. He had soon some orders for the
wheel ; and in 1851 he took the important step of settling down
as a civil engineer in Belfast.

His business grew by degrees. His health improved, and we
find him occupied in the next two or three years with scientific
investigations as to the " properties of whirling fluids." This led
to improvements in the action of blowing fans on the one hand,
and, on the other, to the invention of a centrifugal pump and to
improvements in turbines which were described to the British
Association at Belfast in 1852. At this meeting, also, he described
" A Jet Pump, or Apparatus for drawing up Water by the Power
of a Jet"; and these investigations led to the designing, on the
large scale, of pumps of this kind. Some of these pumps have
done important work in the drainage of low lands at places where
a small stream, capable of supplying the jet, can be found in the
immediate proximity. His investigations on the mechanics of
whirling fluids, again, led to the design of great centrifugal pumps,
the largest of which are now at work on sugar plantations in
Demarara.

It will thus be seen that he was giving much attention to
water engineering; and in November, 1853, he became resident
engineer to the Belfast Water Commissioners, a post which he
occupied till the end of 1857.

In this year he was appointed Professor of Civil Engineering
and Surveying in Queen's College, Belfast. He became fully
occupied with the duties of his professorship, and gave up his
office and business as a civil engineer, except for the connection
which he retained with some of his former clients, and for business
in consultation.

The professorship in Belfast he held till the death of Macquorn
* Roy. Soc. Proc. December 5, 1861.

XCviii OBITUARY NOTICE

Rankine in 1872. By this event the Professorship of Civil Engi-
neering in Glasgow became vacant ; and James Thomson was in
the next year appointed by the Government to succeed him.

In 1888 his sight unfortunately began to fail; and the
malady, from which both his eyes suffered, proceeded so far that
it became necessary for him to resign his University work. This
he did after the end of the session 1888-89. Happily, however,
he retained more or less of his eyesight till the end of his life ;
and as he became more accustomed to the condition of his eyes he
was better able to make use of what remained to him, and was
able to move about freely with but little assistance, and even to
read and write a little, and to make on a large scale the diagrams
which he used to illustrate his Bakerian Lecture on " The Grand
Currents of Atmospheric Circulation."

His death was almost sudden and was the beginning of a
sadly tragic time in his family. In a single week Professor
Thomson, his wife, and youngest daughter were all attacked with
cold, which was quickly followed by inflammation of the lungs.
The next week saw the death of all three ; his daughter surviving
him only three days, and Mrs Thomson seven days. Professor
Thomson's death took place on the 8th of May, 1892.

It is not possible in the limits to which this notice must be
confined to refer to all James Thomson's papers, nor to give a
complete list of the many subjects which occupied his attention.

Already some of his contributions to thermodynamics have
been mentioned; but it must be further remarked that during
the portion of his life which was occupied with teaching, he gave
great attention to this subject, endeavouring to improve the
nomenclature and modes of expression of the various principles
and propositions connected with it, and to simplify modes of
explanation and of statement.

Another very remarkable contribution to thermal science and
thermodynamics was his extension of Andrews' discoveries on the
subject of the continuity of the liquid and gaseous states of
matter. Thomson's mode of conception of the whole subject,
which led to the construction of a model in three dimensions to
show the mutual relations between pressure, volume, and tem-
perature of such a substance as carbon dioxide under continuous
changes of pressure, and volume, and temperature, was perfectly
new and most important. The model itself threw a flood of light

BY DR J. T. BOTTOMLEY XC1X

on the question ; and the imagining of the extension of the three-
dimensional surface so as to include an unstable condition of the
substance, partially realisable and even well known in the phe-
nomena of a liquid passing its boiling point without forming
vapour, and in similar unstable conditions, was an advance in the
theory of this important question, the consequences of which are
not even now completely realised. The verification of Thomson's
theories on this subject has proved a fruitful field of experimental
investigation for many workers.

Another subject of great importance to which Professor James
Thomson devoted much thought and attention was that of safety
and danger in engineering structures, and the principles on which
their sufficiency in strength should be estimated and proved. He
made more than one weighty communication on this subject to
engineering societies ; and on his appointment at Glasgow, in
1873, he made it the subject of the Latin address which it is the
custom for a newly elected Professor to read to the Senatus of the
University of Glasgow. An address in English on the same
subject became his inaugural lecture to the students of his class
in engineering.

When he took up the question, about 1862, he felt that
ordinary engineering practice as to testing of structures, boilers
for example, was both illogical and unsafe. He considered that
the tests usually applied were quite insufficient to permit of an
engineer feeling justified in risking the lives of men and the
property of his employers to the dangers of breakdown. It was
then a common opinion that severe testing should not be applied
lest the structure should be weakened by the test itself; but
Thomson denied that the test does weaken the structure if the
structure be good ; and pointed out that the real reason for not
applying a proper test was, frequently, fear lest the structure
should be found far inferior in strength to that which it was
intended to have. The truth of Professor Thomson's contentions
is now admitted by the highest engineers ; and the best engineer-
ing practice has, happily, undergone a thorough reform in this
respect.

Certain geological questions possessed much interest for James
Thomson. We have seen how, at an early age, he investigated
the parallel roads of Glen Roy; and on many subsequent occa-
sions he examined with great care the places where he chanced to

C OBITUARY NOTICE

be residing, and found and described glacier markings. He traced
out, on more than one occasion, specially interesting features of
the ice action, endeavouring to determine, by means of an exami-
nation of the markings, details as to the motion of the ice,
whether in the form of glacier or in the form of icebergs taking
the ground in shallow waters.

His attention was also directed to the jointed prismatic struc-
ture seen at the Giant's Causeway in Ireland, and elsewhere. No
satisfactory explanation of this remarkable phenomenon had been
given. The old theories, involving a supposed spheroidal concre-
tionary tendency in the material during consolidation, seemed
quite untenable. He examined with great care the appearances
presented in the surfaces of the stones, and concluded that the
columnar structure is due to the shrinking and cracking during
cooling of a very homogeneous mass of material. The cross joints
he considered to be in reality circular conchoidal fractures com-
mencing at the centre of the column and flashing out to the
circumference.

A very interesting subject, and one of very high importance,
to which Professor Thomson gave great attention, is the flow of
water in rivers. He investigated, with great care, and from a
theoretical point of view, the origin of windings of rivers in
alluvial plains, and his conclusions were published in the Proceed-
ings of the Royal Society, May 4, 1876. Later in the same year
he constructed, in clay, on a table, a model with which he investi-
gated the movements of the different parts of the water in passing
round the bends in this artificial river; and, finally, he made a
large wooden model of a river flowing on a nearly horizontal bed
with many bends and various obstacles. By aid of fine threads,
small floating and sinking bodies, and coloured streams of fluid
coming from particles of solid aniline dye dropped into the
channel, he was able to follow from point to point the movements
of the fluid, and thus to give not only beautiful and striking
ocular evidence of the truth of his early conclusions, but also to
extend his theory. Papers on this subject were communicated to
the Royal Society in 1876, 1877, 1878. The paper of the last-
named date was entitled " On Flow of Water in Uniform Regime
in Rivers and in Open Channels generally." It contains a very
clear and striking account of what does occur in the motion of a
river down its inclined channel; and, in particular, of the fact

BY DR J. T. BOTTOMLEY ci

which seems to be ascertained, that the forward velocity of the
water in rivers is, generally, not greatest at the surface with
gradual abatement from surface to bottom (as would be required
under the conditions supposed in the laminar theory) ; but that,
in reality, the average velocity down stream is greatest at some
depth below the surface, from which, up to the surface, there is a
considerable decrease, and down to the bottom a much greater
decrease. This phenomenon he showed very clearly to be due to
the rising of masses of slow-going water, from the bottom, on
account of directing action of bottom obstacles. These masses
of slow-going water, when they reach the top, spread themselves
out, and, mingling with the quicker surface water, give to it, on
the whole, a less rapid movement than it should otherwise possess.
The paper, as a whole, forms a masterly exposition of this important
subject.

Finally, in this brief summary must be mentioned the paper
which was made the Bakerian Lecture for the year 1892. In
1857 Professor Thomson read a paper to the British Association,
on " The Grand Currents of Atmospheric Circulation." It appears
that his attention was first called to this subject when, during the
period of his early delicacy, his father asked him to look into the
question of the Trade Winds and write a short account of this
atmospheric phenomenon for a new edition of Dr Thomson's
Geography, which was then in preparation. This was done ; but
young James Thomson found so little satisfaction in the informa-
tion and theories which he then studied for the purpose that his
mind was keenly directed to the question; and in 1857 he himself
had formed a theory which he expounded to the British Asso-
ciation.

The subject was before his mind during the rest of his life ;
and though on account of other pressing work the complete publi-
cation of the theory was from time to time deferred, yet it was
always his intention to return to the question. When in the last
years of his life the affliction of partial blindness came upon him,
and when he had somewhat recovered from the first depressing
effects of finding himself thus sadly crippled, he set himself in his
enforced leisure to complete this work, and, with the assistance of
his wife and daughters, to produce the important paper which was
read before the Royal Society on the 10th of March, 1892. In
this paper a historical sketch is given of the progress of observa-

Cll OBITUARY NOTICE BY DR J. T. BOTTOMLEY

tion and theoretical research into the nature and causes of the
trade- winds and other great and persistent currents of atmospheric
circulation. Previous theories are discussed and criticised and
their merits duly recognized, the theory of Hadley, in particular,
being shown to be substantially true. A much more complete
theory is then expounded in full detail ; and charts and diagrams
in illustration show the nature of the aerial motions.

Here this memoir must close. There are many papers of
Thomson which have not even been alluded to in it. Nor is it
possible or necessary for the present purpose to refer to all the
subjects to which his ever active mind directed itself. A character
so truly philosophic it is very rare to meet. His was a singularly
well ordered and well governed mind. It was, if one may venture
to say so, almost too philosophical and too well governed for the
business of every-day life. He could scarcely realise a difference
between greater and smaller error or untruth. Great or small
error and untruth were to be condemned and resisted ; and,
perhaps, in the matter of public business and in this hurrying
nineteenth century pressure, there were those who, thoroughly
conscientious themselves, could not yet feel perfect sympathy
with his extreme and scrupulous determination to let nothing,
however small, pass without thorough examination and complete
proof. To temporise was not in his nature ; and this extreme
conscientiousness gave rise to a want of rapidity of action which
was perhaps the only fault in a singularly perfect character.

Purity and honour in word and deed and thought, gentleness
of disposition, readiness to spend his labour, his time, his mental
energies for others, and for the good of the world in general, all
were conspicuous in his life both in public and in private.

Professor Thomson was elected Fellow of the Royal Society in
1877; and he received the honorary degree of D.Sc. from the
Queen's University in Ireland, and of LL.D. from his own Uni-
versity of Glasgow, and from the University of Dublin.

In 1853 he married Elizabeth Hancock, daughter of William
John Hancock, Esq., J.P., of Lurgaii, Co. Armagh, a lady who
devoted herself to every minutest interest of her husband's life.
They had one son and two daughters, of whom the son and elder
daughter survive.

J. T. B.

LIST OF SCIENTIFIC TERMS cm

LIST OF SCIENTIFIC TERMS INTRODUCED BY
PROF. JAMES THOMSON.

1. 1873. Radian, used in General Class Examination, Queen's College,

Belfast, June 5, 1873. See College Calendar : Thomson's
Arithmetic, 1880 edition, p. 62. Cf. correspondence with
Dr Muir, Nature, Vol. 83, pp. 156, 217, 459, 460.

2. 1874. Interface, see Sir W. Thomson, "Kinetic Theory of the Dissipa-

tion of Energy," 1874, Math, and Phys. Papers, Vol. v. p. 12 ;
see also Maxwell, Theory of Heat, 1875 edition, p. 95 ; see
also infra, pp. 65, 424 ; also p. 327, 1869.

3. 1875. Unital, e.g. unital stress proportional to unital strain, see

"Comparisons of Similar Structures," infra, p. 364 note.

4. 1875. Poundal, see Maxwell, Theory of Heat, 1875 edition, p. 83; also

" Flow of Water through Orifices," infra, p. 66 note.

5. 1875. Gravity, instead of weight ; see infra, pp. 362 note, 454.

6. 7. 1876. Crinal, Funal, see "Metric Units," B. A. 1876, infra, p. 373,

also p. 66 note.

8. 1876. Ergometer, instead of dynamometer ; see paper " On an Inte-

grating Machine," K. S. 1876, infra, p. 452 note.

9. 1876. Free Level, see "Flow of Water through Orifices," B. A. 1876,

infra, p. 64, also p. 97.

10. 1878. Change ratio, "Dimensional Equations," B. A. 1878, infra,

p. 375.

11. 1878. Numeric, " Dimensional Equations," B. A. 1878, see infra, p. 376 ;

also Thomson's Arithmetic, 1880 edition, p. 4.

12. 1879. Hesion, for tangential force between two pieces of matter when

there is no motion, see letter to Clerk Maxwell, infra, p. 458.

13. 1880. Ratio Equation ; a statement of the equality of two ratios, see

Thomson's Arithmetic, 1880 edition, p. 95.

14. 1880. Rate Equivalence, see Thomson's Arithmetic, 1880 editior,, p. 108.

15. 1880. Ply, Plication, instead of multiply and multiplication, see

Thomson's Arithmetic, 1880 edition, p. 152.

16. 1880. Disply, for the reverse of Ply, instead of Divide, see Thomson's

Arithmetic, 1880 edition, p. 155.

17. 1880. Round, used for an angle of 360°, see Thomson's Arithmetic,

1880 edition, p. 61.

18. 1882. Forcive, for "any system of force," see Lord Kelvin, Math, and

Phys. Papers, Vol. iv. p. 369 note.

19. 1884. Apocentric force, instead of Centrifugal, see "Whirlwinds and

Waterspouts," B. A. 1884, infra, p. 148.

CIV LIST OF SCIENTIFIC TERMS

20. 1884. Centreward acceleration, instead of centripetal, B. A. 1884 ; see

also infra, p. 69 note, 1876.

21, 22. 1884. Clinure, Posure, see " Law of Inertia," infra, p. 380 note.

23. 1884. Torque, for force-pair or couple, used in printed examination

papers, April 22, 1884 ; see also Transactions of the Insti-
tution of Engineers and Shipbuilders in Scotland, 1885—6,
Vol. xxix. p. 91.

24. 1888. FluiJ "action, see infra, p. 272.

25. 1892. Revolutional Momentum instead of " Moment of Momentum," or

"Angular Momentum," see Bakerian Lecture, infra, p. 191.

26. Expansity, for converse of Density. " Bulkiness of a body

relative to its quantity of matter."

27. Ward, instead of Direction.

28. Ways of Freedom, instead of Degrees of Freedom. *

PAPERS RELATING TO FLUID
MOTION

1. ON SOME PROPERTIES OF WHIRLING FLUIDS [VERTICAL
FREE VORTEX], WITH THEIR APPLICATION IN IMPROVING
THE ACTION OF BLOWING FANS, CENTRIFUGAL PUMPS,
AND CERTAIN KINDS OF TURBINES.

[From the British Association Report, Section G, Belfast, 1852, page 130.]

THE author pointed out several properties possessed by masses
of fluids revolving in the circumstances of one of the most ordinary
kinds of whirlpools, that, namely, which is formed when water is
supplied at the circumference of a widely extended vessel, with
a very slight rotatory motion, and is allowed to flow away by
a central orifice in the bottom. Of these properties, the following,
in which the influence of friction is left out of consideration, may
be cited :

The equation of the curve whose revolution would generate
the curved surface of the whirlpool is y = Cs/a?} where y is the
depth of any point of the curve below the level of the fluid taken
at any part far away from the whirlpool, where there is no per-
ceptible depression ; x the distance of the point from the axis
of revolution ; and C a constant quantity.

Every point of the surface of the fluid moves with the velocity
which a heavy body would attain in falling from the level of the
surface far away from the whirlpool to the level of the point.
Also every point in the interior of the revolving mass moves with
the velocity of the point on the surface vertically above itself;
and it follows, that the velocities of points at various distances
from the centre are inversely proportional to the distances.

T. 1

2* FATFJIS RELATING TO MOTION OF FLUIDS [2

It follows also that the velocity of each point in the mass, is
the greatest that is possible without an increase of the velocity
of every other point revolving further from the centre.

He was led from these and other properties of whirling fluids,
to find that the efficiency of centrifugal pumps for water, and
of fans for causing blasts of air, may be greatly increased by the
provision, outside of the circumference of the wheel, of a space in
which the fluid may continue to revolve without any interruption
after it has left the wheel. He mentioned also, that an apparatus
termed a " diffuser," and involving the same principle, has recently
been applied with good results, in turbines of great power con-
structed in America.

2. ON THE VORTEX WATER-WHEEL.

[From the Report of the British Association, Belfast, 1852, page 317.
A Communication ordered to be printed among the Reports.]

NUMBERLESS are the varieties, both of principle and of con-
struction, in the mechanisms by which motive power may be
obtained from falls of water. The chief modes of action of the
water are, however, reducible to three, as follows: — First, The
water may act directly by its weight on a part of the mechanism
which descends while loaded with water, and ascends while free
from load. The most prominent example of the application of this
mode is afforded by the ordinary bucket water-wheel. Secondly,
The water may act by fluid pressure, and drive before it some
yielding part of a vessel by which it is confined. This is the mode
in which the water acts in the water-pressure engine, analogous
to the ordinary high -pressure steam-engine. Thirdly, The water,
having been brought to its place of action subject to the pressure
due to the height of fall, may be allowed to issue through small
orifices with a high velocity, its inertia being one of the forces
essentially involved in the communication of the power to the
moving part of the mechanism. Throughout the general class of
water-wheels called Turbines, which is of wide extent, the water
acts according to some of the variations of which this third mode
is susceptible. The name Turbine is derived from the Latin word

1852] ON THE VORTEX WATER-WHEEL 3

turbo, a top, because the wheels to which it is applied almost all
spin round a vertical axis, and so bear some considerable resem-
blance to the top. In our own country, and more especially on
the Continent, turbines have attracted much attention, and many
forms of them have been made known by published descriptions.
The subject of the present communication is a new water-wheel,
which belongs to the same general class, and which has recently
been invented and brought successfully into use by the author.

In this machine the moving wheel is placed within a chamber
of a nearly circular form. The water is injected into the chamber
tangentially at the circumference, and thus it receives a rapid
motion of rotation. Retaining this motion it passes onwards
towards the centre, where alone it is free to make its exit. The
wheel, which is placed within the chamber, and which almost
entirely fills it, is divided by thin partitions into a great number
of radiating passages. Through these passages the water must
flow on its course towards the centre ; and in doing so it imparts
its own rotatory motion to the wheel. The whirlpool of water
acting within the wheel-chamber, being one principal feature of
this turbine, leads to the name Vortex as a suitable designation
for the machine as a whole.

The vortex admits of several modes of construction, but the
two principal forms are the one adapted for high falls and the one
for low falls. The former may be called the High-pressure Vortex,
and the latter the Low-pressure Vortex*. Examples of these two
kinds, in operation at two mills near Belfast, are delineated in
figs. 1 and 2, with merely a few unimportant deviations from the
actual constructions.

Figs. 1 and 2 are respectively a vertical section, and a plan of
a vortex of the high-pressure kind in use at the Low Lodge Mill
near Belfast, for grinding Indian cornf. In these figures A A is the
water-wheel. It is fixed on the upright shaft, B, which conveys
away the power to the machinery to be driven. The water-wheel
occupies the central part of the upper division of a strong cast-iron

* These terms correspond to Hochdruckturbine, and Niederdruckturbine, used
in Germany to express the like distinction in turbines.

t This vortex was only in course of erection at the time of the meeting of the
British Association in Belfast. The water-wheel itself, removed from its case,
being light and of small dimensions, was exhibited in Section G. It is composed
chiefly of thick-tinned iron plates united by soft solder.

1—2

PAPERS RELATING TO MOTION OF FLUIDS

[2

case, (7(7; and the part occupied by the wheel is called the wheel-
chamber. DD is the lower division of the case, and is called the
supply chamber. It receives the water directly from the supply
pipe, of which the lower extremity is shown at E, and delivers it
into the outer part of the upper division, by four large openings,
F, in the partition between the two divisions. The outer part of
the upper division is called the guide-blade chamber, from its

Sec/tonal C/e

Fig. 1.

containing four guide-blades, G. which direct the water tangen-
tially into the wheel-chamber. Immediately after being injected
into the wheel-chamber the water is received by the curved
radiating passages of the wheel, which are partly seen in fig. 2,
at a place where both the cover of the wheel-chamber and the
upper plate of the wheel are broken away for the purpose of
exposing the interior to view. The water, on reaching the inner
ends of these curved passages, having already done its work, is
allowed to make its exit by two large central orifices, shown

1852]

ON THE VORTEX WATER-WHEEL

distinctly on the figures at the letters L, L ; the one leading
upwards and the other downwards. It then simply flows quietly
away; for, the vortex being submerged under the surface of the
water in the tail race, the water on being discharged wastes no
part of the fall by a further descent. At the central orifices, close

\\m\ *&J

mm

Fig. 2.

Tart of the. Wheel on a Larger scule.ta shew
The form of the. rones 7iurre ac

joints between the case and the wheel, to prevent the escape of
water otherwise than through the wheel itself, are made by means
of two annular pieces, L, L, called joint-rings, fitting to the central
orifices of the case, and capable of being adjusted, by means of

6 PAPERS RELATING TO MOTION OF FLUIDS [2

studs and nuts, so as to come close to the wheel without impeding
its motion by friction. The four openings, H, H, figs. 1 and 2,
through which the water flows into the wheel-chamber, each
situated between the point or edge of one guide-blade and the
middle of the next, determine, by their width, the quantity of
water admitted, and consequently the power of the wheel. To
render this power capable of being varied at pleasure, the guide-
blades are made movable round gudgeons or centres near their
points ; and a spindle, K, is connected with the guide-blades by
means of links, cranks, &c. (see -the figures) in such a way that,
when the spindle is moved, the four entrance orifices are all
enlarged or contracted alike. This spindle, K, for working the
guide-blades is itself worked by a handle in a convenient position
in the mill ; and the motion is communicated from the handle
through the medium of a worm and sector, which not only serve
to multiply the force of the man's hand, but also to prevent the
guide-blades from being liable to the accident of slapping suddenly
shut from the force of the water constantly pressing them inwards.
The gudgeons of the guide-blades, seen in fig. 2 as small circles, are
sunk in sockets in the floor and roof of the guide-blade chamber ;
and so they do not in any way obstruct the flow of the water.

Mt in fig. 1, is the pivot-box of the upright shaft. It
contains, fixed within it, an inverted brass cup, shown distinctly
on the figure ; and the cup revolves on an upright pin, or pivot,
with a steel top. The pin is held stationary in a bridge, Nt which
is itself attached to the bottom of the vortex-case. For adjusting
the pin as to height, a little cross bridge, 0, is made to bear it up,
and is capable of being raised or lowered by screws and nuts
shown distinctly on the figure. Also, for preventing the pin from
gradually becoming loose in its socket in the large bridge, two
pinching-screws are required, of which one is to be seen in the
figure. A small pipe, fixed at its lower end into the centre of
the inverted brass cup, and sunk in an upright groove in the
vortex-shaft (see the figures), affords the means of supplying oil to
the rubbing surfaces, over which the oil is spread by a radial
groove in the brass. A cavity, shown in the figures, is provided at
the lower part of the cup, for the purpose of preventing the oil
from being rapidly washed away by the water*.

* Great stress has been laid on the supposed necessity for oiling the pivots
of turbines by continental engineers and authors. The author of the present

1852] ON THE VORTEX WATER-WHEEL 7

Four tie-bolts, marked P, bind the top and bottom of the case
together, so as to prevent the pressure of the water from causing
the top to spring up, and so occasioning leakage at the guide-
blades or joint-rings.

The height of the fall for this vortex is about 37 feet, and the
standard or medium quantity of water, for which the dimensions
of the various parts of the wheel and case are calculated, is 540
cubic feet per minute. With this fall and water supply the
estimated power is 28 horse-power, the efficiency being taken at
75 per cent. The proper speed of the wheel, calculated in accord-
ance with its diameter and the velocity of the water entering its
chamber, is 355 revolutions per minute. The diameter of the
wheel is 22| inches, and the extreme diameter of the case is
4 feet 8 inches.

A low-pressure vortex, constructed for another mill near
Belfast, is represented in vertical section and plan in figs. 3
and 4. This is essentially the same in principle as the vortex
already described, but it differs in the material of which the case
is constructed, and in the manner in which the water is led to the
guide-blade chamber. In this the case is almost entirely of wood ;
and, for simplicity, the drawings represent it as if made of wood
alone, though in reality, to suit the other arrangements of the
mill, brick-work, in certain parts, was substituted for the wood.
The water flows with a free upper surface, W, W, into this wooden
case, which consists chiefly of two wooden tanks, A A and BB, one
within the other. The water-wheel chamber and the guide-blade
chamber are situated in the open space between the bottom of the
outer and that of the inner tank, and will be readily distinguished
by reference to the figures. The water of the head race, having
been led all round the outer tank in the space (7(7, flows inwards
over its edge, and passes downwards by the space DD, between the

communication has thus been led to endeavour to find and adopt the best means
for oiling pivots working under water. The oiling, however, is a source of much
trouble; and he has found in the course of his experience, that pivots of the kind
described above, made with brass working on hard steel, and with a radial groove
in the brass suitable for spreading water over the rubbing surfaces, will last well
without any oil being supplied. The rapid destruction, which is commonly re-
ported as having been of frequent occurrence in turbine pivots, he believes may
in many cases have arisen from the employment of an inverted cup like a
diving-bell as one of the rubbing parts, without any provision for the escape of air
from the cup. It is evident that a pivot of this kind, although under water, might
be perfectly dry at the rubbing surfaces.

8

PAPERS RELATING TO MOTION OF FLUIDS

[2

sides of the two tanks. It then passes through the guide-blade
chamber and the water-wheel, just in the same way as was
explained in respect to the high-pressure vortex already described;
and in this one likewise it makes its exit by two central orifices,
the one discharging upwards and the other downwards. The part
of the water which passes downwards flows away at once to the
tail race, and that which passes upwards into the space E within

Fig. 3.

the innermost tank, finds a free escape to the tail race through
boxes and other channels, F and G, provided for that purpose.
The wheel is completely submerged under the surface of the water
in the tail race, which is represented at its ordinary level at YYY,
fig. 3, although in floods it may rise to a much greater height.
The power of the wheel is regulated in a similar way to that
already described in reference to the high-pressure vortex. In

1852]

ON THE VORTEX WATER-WHEEL

9

this case, however, as will be seen by the figures, the guide-blades
are not linked together, but each is provided with a hand-wheel,
H, by which motion is communicated to itself alone.

Fig. 4.

drawn on a, larger
scale to shew flic air
vatiiTtt of the va7ics
more correctly

10 PAPERS RELATING TO MOTION OF FLUIDS [2

In this vortex, the fall being taken at 7 feet, the calculated
quantity of water admitted, at the standard opening of the guide-
blades, is 2460 cubic feet per minute. Then, the efficiency of the
wheel being taken at 75 per cent., its power will be 24 horse-power.
Also the speed at which the wheel is calculated to revolve is 48
revolutions per minute.

In connexion with the pivot of this wheel arrangements are
made which provide for the perfect lubrication of the rubbing
surfaces with clean oil. The lower end of the upright revolving
shaft enters a stationary pivot-box, K, through an opening made
oil-tight by hemp and leather packing. Within the box there is
a small stationary steel plate on which the shaft revolves. Within
the box, also, there are two oil-chambers, one situated above and
round the rubbing surface of this plate, and the other underneath
the plate. A constant circulation of the oil is maintained by
centrifugal force, which causes it to pass from the lower chamber
upwards through a central orifice in the steel plate, then outwards
through a radial groove in the bottom of the revolving shaft to
the upper chamber, then downwards back to the lower chamber,
by one or more grooves at the circumference of the steel plate.
The purpose intended to be served by the provision of the lower
chamber combined with the passages for the circulation of the oil,
is to permit the oil, while passing through the lower chamber, to
deposit any grit or any worn metal which it may contain, so that
it may be maintained clean and may be washed over the upper
surface of the steel plate at every revolution of the radial groove
in the bottom of the shaft. A pipe leading from an oil cistern, L,
in an accessible situation conducts oil to the upper chamber of the
pivot-box ; and another pipe leaves the lower chamber, and
terminates, at its upper end, in a stop-cock, M. This arrangement
allows a flow of oil to be obtained at pleasure from the cistern,
down by the one pipe, then through the pivot-box, and then up
by the other pipe, and out by the cock. Thus, if any stoppage
were to occur in the pipes, it could be at once detected ; or if
water or air were contained in the pivot-box after the first erection,
or at any other time, the water could be removed by the pipe
leading to the stop-cock, or the air would of itself escape by the
pipe leading to the cistern, which, as well as the other pipe, has a
continuous ascent from the pivot-box. Certainty may consequently
be attained that the pivot really works in clean oil.

1852] ON THE VORTEX WATER-WHEEL 11

The author was led to adopt the pivot-box closed round the
shaft with oil-tight stuffing, from having learned of that arrange-
ment having been successfully employed by Kochlin, an engineer
of Miihlhausen. As to the other parts of the arrangements just
described, he believes the settling chamber with the circulation of
oil to be new, and he regards this part of the arrangements as
being useful also for pivots working not under water. In respect
to the materials selected for the rubbing parts, however, he thinks
it necessary to state that some doubts have arisen as to the suit-
ableness of wrought iron to work on steel even when perfectly
lubricated ; and he would, therefore, recommend that a small piece
of brass should be fixed into the bottom of the shaft, all parts
being made to work in the manner already explained.

The two examples which have now been described of vortex
water-wheels adapted for very distinct circumstances, will serve to
indicate the principal features in the structural arrangements of
these new machines in general. Respecting their principles of
action some further explanations will next be given. In these
machines the velocity of the circumference is made the same as
the velocity of the entering water, and thus there is no impact
between the water and the wheel ; but, on the contrary, the water
enters the radiating conduits of the wheel gently, that is to say,
with scarcely any motion in relation to their mouths. In order to
attain the equalization of these velocities, it is necessary that the
circumference of the wheel should move with the velocity which a
heavy body would attain in falling through a vertical space equal
to half the vertical fall of the water, or in other words, with the
velocity due to half the fall ; and that the orifices through which
the water is injected into the wheel-chamber should be conjointly
of such area that when all the water required is flowing through
them, it also may have a velocity due to half the fall. Thus one-
half only of the fall is employed in producing velocity in the water ;
and, therefore, the other half still remains acting on the water
within 'the wheel-chamber at the circumference of the wheel in
the condition of fluid pressure. Now, with the velocity already
assigned to the wheel, it is found that this fluid pressure is exactly
that which is requisite to overcome the centrifugal force of the
water in the wheel, and to bring the water to a state of rest at its
exit, the mechanical work due to both halves of the fall being
transferred to the wheel during the combined action of the moving

12 PAPERS RELATING TO MOTION OF FLUIDS [2

water and the moving wheel. In the foregoing statements, the
effects of fluid friction, and of some other modifying influences,
are, for simplicity, left out of consideration ; but in the practical
application of the principles, the skill and judgement of the
designer must be exercised in taking all such elements as far as
possible into account. To aid in this, some practical rules, to
which the author as yet closely adheres, were made out by him
previously to the date of his patent. These are to be found in the
specification of the patent, published in the Mechanics Magazine
for Jan. 18 and Jan. 25, 1851 (London)*.

* From the Mechanics' Magazine, 18 January, 1851, pp. 45, 46.

[According to the best calculations I have been able to make as to the principal
dimensions of the wheel and case, and the velocity of the wheel, these should be as
follows :

Let Q be the quantity of water in cubic feet per minute, and H the height of
fall in feet.

Then, Total area of entrance orifice or orifices

= -00329 ~ square feet.
V"

Diameter of each central orifice of the movable wheel

Diameter of the wheel, if the vanes be straight =3 '5 times the diameter of each
central orifice of the wheel.

Diameter of the wheel, if the vanes be curved = twice the diameter of each
central orifice of the wheel.

Revolutions per minute if the vanes be straight

Revolutions per minute if the vanes be curved

Again ; to determine the angle which the inner end of each vane should make
with the radius passing through it :

Let c — circumference of each central orifice in feet ;

d = distance in feet between the top and the bottom plate of the wheel,
minus the thickness of the plate for attaching the vanes to the shaft ;
t = thickness of each vane in feet (or fractions of a foot);
n = number of vanes which terminate at the circumference of the central

orifice ;
v = velocity of the inner end of each vane in feet per minute.

1852]

ON THE VORTEX WATER-WHEEL

13

In respect to the numerous modifications of construction and
arrangement which are admissible in the Vortex, while the leading
principles of action are retained, it may be sufficient here merely
to advert — first, to the use (as explained in the specification of the
patent) of straight instead of curved radiating passages in the
wheel ; secondly, to the employment, for simplicity, of invariable
entrance orifices, or of fixed instead of movable guide-blades ; and
lastly, to the placing of the wheel at any height, less than about
thirty feet, above the water in the tail race, combined with the
employment of suction pipes descending from the central discharge

Also let C, fig. 5, be the centre of the wheel ; DSG part of its outer circum-
ference ; NFB part of the circumference of one of its central orifices ; and let F
be the termination of one vane, and K that of the next which reaches to the
circumference of the central orifices.

Make TH perpendicular to FC, and such that

::-: v.

cd

Then FH would be the direction of the inner end of the vane passing through F,
if the vanes were infinitely thin. To correct for the thickness make

FT-.FO::-^:

cd

cd--

nid

cos HFT

Fig. 5.

Draw OP equal and parallel to TH. FP is the true direction of the end of the
vane.

Again ; draw FL perpendicular to FP, and a little longer than FC. It may be
about =1-2 FC. From L, as centre, describe an arc of a circle FR, terminating at
R in the continuation of CK. FR is the inner portion of the vane, and in forming
the remaining portion, all that need be attended to, is to give it a gentle curvature,
and to make a short portion of it at S be in the direction of a radius passing
through S.}

14 PAPERS RELATING TO MOTION OF FLUIDS [2

orifices, and terminating in the water of the tail race, so as to
render available the part of the fall below the wheel.

In relation to the action of turbines in general, the chief and
most commonly recognized conditions, of which the accomplish-
ment is to be aimed at, are that the water should flow through
the whole machine with the least possible resistance, and that it
should enter the moving wheel without shock, and be discharged
from it with only a very inconsiderable velocity. The vortex is in
a remarkable degree adapted for the fulfilment of these conditions.
The water moving centripetally (instead of centrifugally, which is
more usual in turbines) enters at the period of its greatest velocity
(that is, just after passing the injection orifices) into the* most
rapidly moving part of the wheel, the circumference ; and, at the
period when it ought to be as far as possible deprived of velocity,
it passes away by the central part of the wheel, the part which
has the least motion. Thus in each case, that of the entrance
and that of the discharge, there is an accordance between the
velocities of the moving mechanism and the proper volocities of
the water.

The principle of injection from without inwards, adopted in
the vortex, affords another important advantage in comparison
with turbines having the contrary motion of the water; as it
allows ample room, in the space outside of the wheel, for large and
well-formed injection channels, in which the water can be made
very gradually and regularly to converge to the most contracted
parts, where it is to have its greatest velocity. It is as a con-
comitant also of the same principle, that the very simple and
advantageous mode of regulating the power of the wheel by the
movable guide-blades already described can be introduced. This
mode, it is to be observed, while giving great variation to the
areas of the entrance orifices, retains at all times very suitable
forms for the converging water channels.

Another adaptation in the vortex is to be remarked as being
highly beneficial, that namely according to which, by the balancing
of the contrary fluid pressures due to half the head of water and
to the centrifugal force of the water in the wheel, combined with
the pressure due to the ejection of the water backwards from the
inner ends of the vanes of the wheel when they are curved, only
one-half of the work due to the fall is spent in communicating
vis viva to the water, to be afterwards taken from it during its

1852] ON THE VORTEX WATER-WHEEL 15

passage through the wheel; the remainder of the work being
communicated through the fluid pressure to the wheel, without
any intermediate generation of vis viva. Thus the velocity of the
water, where it moves fastest in the machine, is kept comparatively
low ; not exceeding that due to half the height of the fall, while
in other turbines the water usually requires to act at much higher
velocities. In many of them it attains at two successive times the
velocity due to the whole fall. The much smaller amount of action,
or agitation, with which the water in the vortex performs its
work, causes a material saving of power by diminishing the loss
necessarily occasioned by fluid friction.

In the Vortex, further, a very favourable influence on the
regularity of the motion proceeds from the centrifugal force of the
water, which, on any increase of the velocity of the wheel, increases,
and so checks the water supply ; and on any diminution of the
velocity of the wheel, diminishes, and so admits the water more
freely ; thus counteracting, in a great degree, the irregularities of
speed arising from variations in the work to be performed. When
the work is subject to great variations, as for instance in saw- mills,
in bleaching works, or in forges, great inconvenience often arises
with the ordinary bucket water-wheels and with turbines which
discharge at the circumference, from their running too quickly
when any considerable diminution occurs in the resistance to their
motion.

The first vortex which was constructed on the large scale was
made in Glasgow, to drive a new beetling-mill of Messrs C. Hunter
and Co., of Dunadry, in County Antrim. It was the only one in
action at the time of the Meeting of the British Association in
Belfast ; but the two which have been particularly described in the
present article, and one for an unusually high fall, 100 feet, have
since been completed and brought into operation. There are also
several others in progress; of which it may be sufficient to
particularize one of great dimensions and power, for a new flax-
mill at Ballyshannon in the West of Ireland. It is calculated for
working at 150 horse-power, on a fall of 14 feet, and it is to be
impelled by the water of the River Erne. This great river has an
ample reservoir in the Lough of the same name ; so that the water
of wet weather is long retained, and continues to supply the river
abundantly even in the dryest weather. The lake has also the
effect of causing the floods to be of long duration, and the vortex

16 PAPERS RELATING TO MOTION OF FLUIDS [4

will consequently be, through a considerable part of the year, and
for long periods at a time, deeply submerged under back-water.
The water of the tail race will frequently be 7 feet above its
ordinary summer level ; but as the water of the head race will
also rise to such a height as to maintain a sufficient difference of
levels, the action of the wheel will not be deranged or impeded
by the floods. These circumstances have had a material influence
in leading to the adoption in the present case of this new wheel
in preference to the old breast or undershot wheels.

3. ON A CENTRIFUGAL PUMP AND WINDMILL ERECTED* FOR
DRAINAGE AND IRRIGATION IN JAMAICA.

[From the British Association Report, Section G, Glasgow, 1855, page 210.]

IN this paper Mr Thomson gave explanations, with the aid
of large drawings, of a centrifugal pump recently constructed,
embodying the improvement of an exterior whirlpool which he
had first made public in the Mechanical Section at the Belfast
Meeting in 1852*. He also described a windmill, with its
framing of very simple construction, which had been specially
designed for working the pump. The apparatus was prepared
for purposes of drainage and irrigation in Jamaica, the costliness
of fuel and the habitual use of windmills in that island having
led to the selection of the windmill in this case as the source
of power. The whole apparatus was constructed in Glasgow and
afterwards erected and brought into action at its destination.

4. ON A CENTRIFUGAL PUMP WITH EXTERIOR WHIRLPOOL,
CONSTRUCTED FOR DRAINING LAND.

[From the Proceedings of the Institution of Engineers in Scotland,
October 27, 1858.]

THE centrifugal pump which forms the subject of the present
communication has been designed and constructed in the course
of this year, for Messrs James Ewing & Co. of Glasgow, for the
drainage of lands belonging to them in Demerara.

The cultivated district of Demerara in which the lands referred
* [Supra, p. 2.]

1858] ON A CENTRIFUGAL PUMP WITH EXTERIOR WHIRLPOOL 17

to are situated, forms a narrow strip or belt of low ground extend-
ing along the sea-coast. It is about four or five miles wide, as
measured from the sea back towards the interior. It lies generally
below the level of high tide ; and is protected in front against the
waters of the sea, and in rear against the waters of the Savannahs,
or inland swamps, by embankments. The district was originally
embanked and reclaimed by the Dutch, and was taken from them
by the English in 1796, along with other parts of what now forms
British Guiana. The drainage is ordinarily effected by valves or
kokers, as they are designated, which discharge to the sea when
the tide is low, but hinder the entrance of the tidal water when
it rises. Of late years banks of soft and shifting mud, or slob,
have been gathering and increasing for great distances out to sea,
for miles perhaps, in front of some of the estates. These banks,
by stopping the drainage outlets to the sea, have caused several
estates to be swamped, and have been threatening like destruction
to others. Some estates, it is understood, have been saved, mainly
by the employment of centrifugal pumps driven by steam power,
which keep up the drainage when the slob rises so high as to stop
the ordinary flow to the sea by gravitation through the valves or
kokers; and which, by keeping, up a run of wa,ter over the slob,
tend, as is believed, in a material degree, to keep open the outlet
channels through the slob, or to open them again when choked
up by the shifting of the mud banks. Some of the estates of
Messrs James Ewing & Co., after having been seriously threatened
for several years by the approach of mud banks to their front,
were last year partially injured by deficient drainage; and thus
the proprietors were led to determine on speedily procuring
a centrifugal pump, to be driven by a steam-engine already
existing on their land, as the driving power for one of their sugar
mills. They engaged the writer to prepare the designs according
to an improved arrangement, which had been devised by him for
increasing the work done by a given power, the main feature
of which is the employment of an exterior whirlpool round the
circumference of the pump wheel. The exterior whirlpool had
been previously introduced in a centrifugal pump designed by
him in 1853, for Messrs James Ewing & Co., for drainage of
lands on an estate of theirs in Jamaica, and constructed by
Messrs W. & A. M'Onie & Co. of Glasgow. It had also more
recently been introduced in a centrifugal pump constructed
T. 2 -

18 PAPERS RELATING TO MOTION OF FLUIDS [4

according to his designs by Messrs Robert Napier & Sons, for
a steamer for the Great West of Scotland Fishery Company*.
The nature of this modification in centrifugal pumps, consisting
of the introduction of the exterior whirlpool, may be understood
from the following explanations :

In centrifugal pumps for water, or fans for air, when doing

actual work in lifting the fluid, or in forcing it against a pressure,

the fluid has necessarily a considerable tangential velocity on

leaving the circumference of the wheel. This velocity in wheels

in which the vanes or blades are straight and radial, is the

same as that of the circumference of the wheel ; in others, in

which the vanes are curved backwards in receding from the

centre, it is somewhat less ; but in all cases it is so great that the

water on leaving the wheel carries away, in its energy of motion,

a large and important part of the work applied to the wheel by

the steam-engine, or other prime mover. This energy of motion

in centrifugal pumps and fans, as ordinarily constructed, is mainly

consumed in friction and eddies in the discharge pipe, which

receives the water or air directly from the circumference of the

wheel. The object of the introduction of the exterior whirlpool is

to prevent this waste, and to apply usefully, towards increasing

the pumping power, the energy of the motion inherent in the

fluid on its leaving the circumference of the wheel. For this

purpose there is provided, round the circumference of the wheel,

an exterior chamber, in which the fluid is left free to revolve, in

virtue of the motion it had on leaving the wheel. This chamber

may be called the exterior whirlpool chamber, and its diameter is

ordinarily made about double that of the wheel. The fluid

revolving in it assumes the condition of a vortex or whirlpool,

which has been designated by the writer as the Vortex or

Whirlpool of free mobility. The principles of the motion of this

kind of whirlpool, and of its application in improving the action

of centrifugal pumps and blowing fans, was first brought forward

at the Belfast Meeting of the British Association in 1852, in a

paper read in the Mechanical Section, of which an abstract is to

be found in the Report of the Meetingf . The chief properties for

which this whirlpool is remarkable, are, that its particles move

with velocities inversely proportional to their distances from the

* See Transactions of the Institution of Engineers in Scotland, Vol. i. p. 90.
t [Supra, p. 1.]

1858] ON A CENTRIFUGAL PUMP WITH EXTERIOR WHIRLPOOL 19

centre or axis of rotation, and that each particle composing it
is free to move to any position within the whirlpool, without
interfering with the general motion of the other particles, as each
one in moving towards or from the centre assumes of itself, subject
simply to the laws of motion under a central force, the velocity
due to its position in the whirlpool. It is also a property of this
whirlpool, that, for any equal particles, in whatever situations in
it they may momentarily be, the sum of the energies corresponding
to velocity, to pressure, and to height, is constant. Thus it arises
that, in the exterior whirlpool in the pump for raising water, as
each particle of the water in moving from the centre, gives up its
velocity according to the law of motion already stated, it either
actually ascends or becomes subject to a pressure capable of
causing it to ascend, through a height corresponding to the energy
deducted from its motion. It follows, therefore, that through the
medium of the exterior whirlpool a decided increase in the
working efficiency of centrifugal pumps is attainable ; the work
contained in the rapid motion of the water leaving the wheel,
which in centrifugal pumps as ordinarily constructed is wasted,
being, according to the new arrangement, usefully employed in
increasing the pumping power of the machine.

To arrive by a simpler method, than that just given, at a
general idea of the mode of action of the exterior whirlpool in
improving the efficiency of the centrifugal pump, it is only
necessary to consider that the mass of water revolving in the
whirlpool chamber, round the circumference of the wheel, must
necessarily exert a centrifugal force, and that this centrifugal
force may readily be supposed to add itself to the outward force
generated within the wheel ; or, in other words, to go to increase
the pumping power of the wheel. The outward force generated
within the wheel is to be understood as being produced entirely
by the medium of centrifugal force, if the vanes of the wheel
be straight and radial; but if they be curved, as is more
commonly the case, the outward force is partly produced through
the medium of centrifugal force, and partly applied by the vanes
to the water, as a radial component of the oblique pressure,
which, in consequence of their obliquity to the radius, they apply
to the water as it moves outwards along them. On this subject
it is well to observe, that while the quantity of water made to
pass through a given pump with curved vanes is perfectly variable

2—2

20 PAPERS RELATING TO MOTION OF FLUIDS [4

at pleasure, the smaller the quantity becomes the more nearly
will the force generated within the wheel for impelling the water
outwards, become purely centrifugal force, and the more nearly
will the pump become what the name ordinarily given to it would
seem to indicate — a purely centrifugal pump. When, however, a
centrifugal pump with vanes curved backwards in such forms as
are ordinarily used in well-constructed examples of the machine,
is driven at a speed considerably above that requisite merely to
overcome the pressure of the water, and cause lifting or propulsion
to commence, the radial component of the force applied to the
water by the vanes will become considerable, and the water
leaving the circumference of the wheel will have a velocity less
than that of the circumference of the wheel, in a degree having
some real importance in practice. It has, indeed, been pro-
mulgated in respect to some centrifugal pumps with curved vanes
brought into use in the last six or eight years, that they are
capable of propelling the water from the centre to the cir-
cumference, along the line of a stationary radius, and of
discharging the water at the circumference without rotatory
velocity. This supposition needs only to be mentioned as being
fallacious. A motion approximately along a stationary radius
may no doubt have been attained when the pump was made to
impel a fluid against no resistance ; but when a pump is actually
doing work in raising water, the rotatory motion of the water on
leaving the circumference of the wheel is unavoidable. In practice
it involves, in ordinary pumps, an important loss, the loss being
commonly about as much as the entire power usefully applied in
overcoming the gravitation of the water ; and the efficiency of the
pump comes out, therefore, when friction and other further losses
are taken into account, in ordinary circumstances, considerably
less than fifty per cent, of the applied power.

From calculations relative to the various sources of loss
occurring in centrifugal pumps of the improved kind with the
exterior whirlpool, according to the design carried out for
Messrs James Ewing & Co. — the writer thinks the efficiency of
such pumps may be fairly estimated at about seventy per cent.
Now the steam-engine, already existing on the estate, for which
the pump forming the special subject of the present paper was
required, is estimated as being capable of applying 25 horse-
power (of 33,000 foot-pounds per minute) to the driving of the

1858] ON A CENTRIFUGAL PUMP WITH EXTERIOR WHIRLPOOL 21

pump. The lift of the water is intended to be variable, according
to the state of the weather, and is to range ordinarily from
2J feet to 5 feet. Then for a 2-J- feet lift, and an assumed
efficiency of the pump of seventy per cent., the quantity of water
lifted comes to be 3700 cubic feet per minute. And for a lift
of 5 feet, the quantity would be about half as much, or, say 1850
cubic feet per minute.

The details of the constructive arrangements of the centrifugal
pump are shown in figs. 1 and 2, prepared from drawings supplied
to the Institution by Messrs W. & A. M'Onie & Co., the engineers
by whom the execution of the work has been carried out. In
reference to them, the writer here wishes to recognize the very
efficient aid they afforded him during the progress of the work in
arranging many of the practical details of the construction. The
work was required to be designed and executed in great haste,
and their ready co-operation tended very materially to facilitate
the business of the undertaking. Fig. 1 is an elevation, and
fig. 2 is a plan of the pump — one-half of each figure being in
section — fig. 1 as through the line a b in fig. 2, and fig. 2 as
through the line c d in fig. 1. In addition to the description
already given of the principles and mode of action of pumps of
this kind, attention may be directed to the helical outlet chamber,
B C, which is arranged for receiving the water from all parts of the
circumference of the whirlpool chamber, except the part from
which an immediate outlet into the discharge pipe is available.
This helical chamber has a gradually increasing area to meet the
regular accessions of water which it receives from its commence-
ment at its smaller extremity, B, forward to its termination at C
in the outlet pipe. This helical outlet chamber is arranged with
a large part of its capacity lying nearer to the axis of rotation
than the edge of the whirlpool chamber cover, D. This arrange-
ment is made with the special object in view of preventing
eddying water that will exist in the outlet pipe at times when
the pump is raising a small quantity of water through a high lift,
from being able to return to the circumference of the whirlpool,
with the risk of breaking through the water of the whirlpool, and,
as it were, falling in towards the centre in consequence of having
less rotatory motion, and, therefore, less centrifugal force than the
water of the whirlpool. If any such return water were to
penetrate into the whirlpool, it would very materially damage

22

PAPERS RELATING TO MOTION OF FLUIDS

1858] ON A CENTRIFUGAL PUMP WITH EXTERIOR WHIRLPOOL 23

the action of the whirlpool, by disturbing its motion, and intro-
ducing impacts of quickly-moving against slowly-moving water.
The helical chamber, as may readily be seen by consideration of
the figures, is adapted for receiving any such eddying water, and
hindering it from getting access to the whirlpool; as the most
rapidly moving water coming direct from the whirlpool will tend
always to fly outwards, and will occupy the outer parts of the
helical chamber, leaving the inner parts of the same chamber for
the dead or eddying water, when from any of the varying circum-
stances of the height of lift and power applied, such eddying or
dead water exists.

The writer would further direct attention to the peculiar
adaptation of the forms selected for the various parts of the case
for the attainment of a high degree of stiffness for preventing the
top and bottom of the case from changing their distance apart
under varying circumstances of the internal water pressure. It is
to be observed, on this point, that no tie-bolts through the case
for holding the top and bottom together are admissible, as any
such tie-bolts would interrupt the revolving motion of the water.
Yet, at the same time, there ought to be as close a fit as possible,
without rubbing, between the joint-rings of the wheel and case at
the central orifices, in order to prevent leakage and waste of the
water pumped. The conical forms of the bottom, E, and top, D, of
the whirlpool chamber, and the cylindrical vertical walls, G, with
the somewhat conical form of the roof, H, of the helical chamber,
all taken together, and, in conjunction with riveted boiler-plate
as the material, form a shell of peculiar stiffness. The chief
difficulty connected with this undertaking has had reference to
the transmission by sea and land of so bulky a thing as the
boiler-plate casing, which is 16 feet in diameter, and which could
not well be sent in parts, to be put together at the site where the
pump is to work. The casing was, of course, sent separate from
the boat, K, or large conduit for leading the water to the lower
central orifice, L, and the casing was shipped on deck, being too
large to enter the hold of the vessel by which it was transmitted.
Accounts have been received of the safe landing in the colony of
these bulky parts ; and news is soon expected of further progress
having been made towards their erection at the site where they
are intended to operate.

It may be mentioned that the pivot, M, on which the wheel, A,

24 PAPERS RELATING TO MOTION OF FLUIDS [5

turns, is made of lignum vitae. It is fixed standing upright in the
bottom of the boat, K ; and in the bottom of the shaft, 0, there is
fixed a brass socket, P, which turns on the pivot. Arrangements
are made for spreading an ample supply of water over the rubbing
surfaces of the wood and brass, for lubrication. Bearings of
lignum vitae have of late years been found to be much superior
in durability, when working under water, to any kinds of metallic
pivots. Lignum vitae, from this reason, has recently come much
into use for the bearings of propeller shafts, where the shafts pass
through the sterns of steamers. Lignum vitae pivots have likewise
come much into use for turbines in America, and the writer is
now in the habit of introducing them in his vortex turbines, in
preference to all other kinds of pivots.

In conclusion, the writer considers centrifugal pumps, con-
structed on the principles which have been described, to be
capable of affording the best available means of raising large
quantities of water through low lifts, or through lifts of such
moderate height as may not require the wheel to revolve at an
inconveniently high speed. For drainage of fens, and for raising
the sewerage of towns through moderate lifts, they are peculiarly
suitable. They are much less liable than common pumps to be
choked or injured by the entrance of solid materials; and, having
no working valves or pistons, they are remarkably free from
injury by wearing; whilst, as regards economy of power in the
applications referred to, they will, the writer believes, be found
decidedly superior to pumps of the ordinary kinds, constructed
with valves and pistons or plungers.

5. ON THE FRICTION BREAK DYNAMOMETER.

[From the Report of the British Association, Section G, Glasgow, 1855,

p. 209.]

IN this paper Mr Thomson explained the nature and principles
of the Friction Break Dynamometer, characterizing it as a highly
valuable apparatus for the measurement of mechanical power.
He turned special attention to matters having important bearings
on its successful employment in practice, and to the consideration
of which he had been led by experience in its use on the large
scale.

1855] ON THE FRICTION BREAK DYNAMOMETER 25

The chief difficulties to be contended with, he stated as
follows :

1. The heat generated in the consumption of the mechanical
power.

2. Vibration or even entire instability of the arm of the break
due to ovalness or other imperfections of the friction drum.

3. Tremor of the driving shaft occasioned by alternate sticking
and slipping of the drum in its friction blocks, instead of steady
slipping.

In regard to these matters he made statements and explana-
tions to the following effect : — Unless the drum be very large with
reference to the power to be consumed by it, the heat generated
by the friction usually requires to be carried off by streams of
water carefully distributed over the drum. On the proper
distribution of the water, and its regularity of supply, much of
the success of the apparatus depends, since great irregularities
in the friction are liable to result from imperfect arrangements
for the water supply.

In the practical employment of the friction break dynamometer
it is often necessary to form the drum in two halves, in order that
it may be got into its place on the driving shaft. This arrange-
ment, however, is often a source of great detriment to the
working of the apparatus, on account of the difficulty or im-
possibility of bringing the two halves of the divided drum so
correctly together as to form a sufficiently perfect cylindrical
surface for producing a uniform friction. In cases therefore in
which the dividing of the drum cannot be avoided, the greatest
possible care ought to be taken in effecting a correct and secure
union of the two parts. He had on some occasions diminished
very materially the inconvenience arising from the vibrations
of the arm, by connecting a spring balance with the scale for
bearing the weights, in such a way as to make the arm tend to
stable equilibrium in the position intended for it when working.

It very frequently happens that, from no clearly apparent
or controllable cause, a violent torsional tremor occurs in the
friction drum and driving shaft ; while through some very slight
change of circumstances, such as a change in the heat of the
drum, or in the mode of application of the water, or in the speed
of revolution of the shaft, steadiness of motion may be instantly
restored, and perhaps soon again destroyed. The origin of the

26 PAPERS RELATING TO MOTION OF FLUIDS [7

tremor he attributes to one of the known laws of the friction and
cohesion of bodies ; namely, that the force necessary to overcome
the cohesion before sliding has commenced, is usually more than
the force necessary to overcome the friction of the sliding motion.
The evil liable to arise from the tremor he had found to be very
great, the danger to life of the by-standers in such experiments
being sometimes considerable. He had himself witnessed a case
in which a violent tremor occurred in the testing of a powerful
water-wheel; and, on the conclusion of the experiments, the
working shaft of the wheel was found to be split and twisted.
Notwithstanding the difficulties occasionally arising in the use
of the friction dynamometer, however, its remarkable efficiency,
when not marred by such occurrences, and the certainty of its
indications when working properly, render it a most valuable
apparatus for practical use in many important and delicate cases
often arising for decision. It is therefore a mechanism in which
improvements are much to be desired ; and also in which, he is of
opinion, they are likely to be found.

6. ON A JET PUMP, OR APPARATUS FOR DRAWING UP WATER
BY THE POWER OF A JET.

[From the British Association Report, Section G, Belfast, 1852, page 130.]

THE purpose for which the author has designed this new
pump, is to clear the water out of the pits of submerged water-
wheels, when access to them is required for inspection or repairs.
This pump may also be used for raising water in other cases
where an abundant fall of water is available ; as, for instance, for
draining a marsh in the neighbourhood of a waterfall. Its action
depends on two principles. One of these is the same as that
of the steam blast used in locomotive engines, and in the ventila-
tion of mines. The other is that of the increased flow of water
from a pipe, produced by giving a gradually widening form to its
discharging extremity.

A sketch of the apparatus is given in the accompanying figure,
where A is a pipe which supplies the water to the nozzle B for the
jet, and C is a pipe which receives, at its narrow end, the jet from

1853]

ON THE JET PUMP

the nozzle, and on account of its gradually widening form, causes
a suction capable of raising water by the pipe D.

The various principles brought into action in this apparatus
have, as was stated by the author, been long known in hydro-
dynamics ; but their combination in this form for use he believed
to be new. A rush of water had been used previously in a

somewhat similar way in Italy to draw up and carry off the water
of a marsh. In respect to the method there employed he had not
been able to obtain full information ; but the description of it he
had received led him to suppose that it was not so efficacious as
the method which formed the subject of his communication to
the Meeting.

7. ON AN EXPERIMENTAL APPARATUS CONSTRUCTED TO DETER-
MINE THE EFFICIENCY OF THE JET PUMP ; AND A SERIES OF
RESULTS OBTAINED.

[From the Report of the British Association, Section G, Hull, 1853, page 130.]

MR THOMSON had last year given, at the Mechanical Section,
an account of a very simple machine which he had contrived for
the purpose of raising water from beneath the lowest available
level of discharge, by means of a supply of other water coming
from a higher level. This machine he designated a Jet Pump,
because it raised water by the action of a jet. A drawing and an
explanation of it, in its original form, are to be found in the
Report of the Transactions of the Mechanical Section for last

28 PAPERS RELATING TO MOTION OF FLUIDS [7

year. The machine is remarkably simple and free from liability
to derangement, having no valves, pistons, or other moving
mechanisms. It consists indeed only of pipes with an internal
jet, and is capable of working properly when left entirely to itself
without the care of an attendant. It had at first been intended
chiefly for one especial purpose, namely, to empty the pits of his
own patent vortex water-wheels, or other submerged turbines,
when access to them is required for inspection or repairs. During
the progress of the trials, however, which were made of it for this
purpose, it soon gave indications of being suitable for much more
extensive uses, and of being likely to prove, in certain cashes, an
advantageous machine for draining swampy lands or shallow lakes.
The cases of this kind for which its employment was contemplated
are those in which the low ground to be drained happens to have,
adjacent to its margin, streams or rivers descending from higher
ground. With a view to determine its efficiency and its appli-
cability in any particular cases of this kind, Mr Thomson had
recently constructed an experimental apparatus in which a jet
pump could be made to act subject to great variations in the ratio
of the height of lift to the height of fall ; and which was suited
for indicating accurately the quantity of water lifted, and the
height of the lift, corresponding to each quantity of water allowed
to fall through any given distance within the working range of the
apparatus. The results obtained give higher efficiencies than had
been anticipated previously to the experiments, and remove all
doubt as to the quantity of water which can be raised in any
ordinary cases of its employment for the drainage of swampy land.
They give, in fact, when taken in conjunction with known laws of
the flow of fluids through orifices, the means of calculating, with
full confidence, the requisite dimensions and proportions of a
machine for the performance of a stated amount of work in the
raising of water.

With respect to the nature of the experiments, a statement of
a few principal points will here suffice, as the form and construction
of the apparatus cannot be minutely explained in the absence of
the drawings, which were exhibited in the Section by the author.

One of the chief difficulties anticipated by Mr Thomson, in
his attempts to find good modes of experimenting, had reference
to the determination of the quantity of water lifted by the pump
from the low level to the discharge level, and of that let down

1853] ON THE JET PUMP 29

from the high level to the discharge level. A very simple and
effective mode of obviating the difficulty was devised, as follows : —
An apparatus was arranged, not for measuring the absolute
quantities of water lifted and let down in various experiments,
but only the ratios of these quantities to one another ; and it is to
be observed, that, for the purpose in view, precision in the ratios
of the quantities, rather than in their absolute amounts, was to be
desired.

A vessel or cistern was provided and set up at a level above
the jet pump ; and all the water to supply the pump, as well as all
the water to be lifted by it, was made to pass through the cistern,
and to issue by a slit in its bottom, about one foot long, and of
a width which could be varied at pleasure, but was usually about
one-quarter of an inch. The water thus issued in the form of
a thin sheet one foot wide and about one-quarter of an inch thick
descending vertically. Out of this sheet of water any portion
desired could be taken and conveyed away by means of a small
movable wedge-shaped vessel made to slide in below the slit
of the cistern. The water thus abstracted was conveyed down to
the low level to be lifted by the jet pump, and the remainder was
used for supplying the power in the jet pump. By observation of
the width of the portion of water abstracted from the sheet, and
comparison of that with the width of the whole sheet, the ratio
of the two quantities was determined.

The absolute quantities of water could be varied at pleasure,
without any alteration of their ratio, by increasing or diminishing
the depth of water in the supply cistern from which the sheet of
water issued. Thus the absolute quantity was adjusted so as
to make either the high water supplying the power, or the low
water lifted by the pump, stand at any desired level while the
pump was in continuous action. The one of those two levels
being thus fixed, the other, after some fluctuations, soon adjusted
itself to its permanent height, and the two permanent levels were
then observed, and so one experiment was completed. The series
of experiments was made by successively cutting out various
portions of the sheet of water to be conveyed to the low level ;
and then observing the height of lift, and the height of fall, which
corresponded to each ratio of the quantity sent to be lifted, to the
quantity sent to supply the power.

The following table gives a summary of the chief practical

30

PAPERS RELATING TO MOTION OF FLUIDS

[8

results obtained. It is derived from two sets of experiments made
on a jet pump with a jet of seven-eighths of an inch diameter.
The height of fall varied from twenty-one inches to twenty-eight
and three-fourths inches, and the height of lift from six inches to
thirty-six and a half inches.

Ratio
of lift
to the
fall

Quantity of
water lifted if
the water sup-
plying the
power is 100

Mechanical
work performed
in the raising
of water if the
work due to
the fall is 100

Ratio
of lift
to the
fall

Quantity of
water lifted if
the water sup-
plying the
power is 100

Mechanical
work performed
in the raising
of water if the
work due to
the fall is 100

0-2

51

10-3

ro

18

18*-0

0-3

44

13-2

ri

16

17-9

0-4

37

14-8

1-2

15

17-6

0-5

33

16-3

1-3

13

17-3

0-6

29

17-3

1-4

11-5

16-3

0-7

26

18-1

1-5

10-2

15-3

0-8

23

18-2

1-6

9-0

14-2

0-9

20

18-1

1-7

7-7

13-2

8. ON THE JET PUMP AND ITS APPLICATION TO THE
DRAINAGE OF SWAMPY LANDS AND SHALLOW LAKES.

[From MS. notes of a paper read at the Royal Dublin Society,
1st June, 1855.]

IN this paper I propose to explain a novel application of a set
of Jet Pumps to the drainage of swampy lands or shallow lakes.

The Jet Pump is a new machine which I brought under the
notice of the Mechanical Section of the British Association at
Belfast in 1852*. At that time I intended it chiefly for use
in draining the water from the pits of turbine water-wheels
when access to them is required for inspection or repairs, and
about the same time I got one introduced at Strabane with very
advantageous results for clearing an excessive amount of soakage
or spring water from a pit in which the building of foundations
for one of my improved turbines was in progress. At that time
I made the jet act horizontally.

* [See supra, p. 26.]

1855] ON THE JET PUMP 31

I subsequently observed that the fall from discharge end
might be saved by addition of a descending pipe dipping below
lowest water level.

This constituted a material improvement and led me at once
to the form in which I now intend that the machine should be
generally used, with the jet acting vertically and the discharge
end of the pipe dipping under the water level in the course
prepared for leading the whole water away from the machine.

A preliminary idea of the principle of action in the jet pump
may probably be best communicated by reference to the jet blast
of locomotive steam engines, which to many must be already
familiar. The waste steam after having left the working cylinders
in the locomotive engine is directed vertically upwards at the
bottom of the chimney in its centre. It mixes with the smoke
and gaseous matters contained in the chimney and dashes them
upwards and thereby produces the draught required for brisk
combustion in the furnace.

Now if we imagine a jet of water to be substituted instead of
the steam as the impelling power, and water also to be substituted
for the products of combustion as the substance to be acted on,
we derive a primary conception of the mode of action of the jet
pump.

For the attainment of a great increase of power, however, and
of a high degree of perfection, an additional principle is introduced.
It consists in causing the water to flow, from its point of greatest
rapidity, forwards, through a gradually enlarging or trumpet-
shaped pipe : — a principle which has the effect of applying usefully
the mechanical work or energy of motion retained in the momentum
of each portion of the united stream proceeding from the jet and
from the low source, in the propulsion of those portions of the
streams which are following.

The principle according to which, when water enters rapidly
at the small end of a gradually widening pipe and flows forwards
to the wide end, each portion of the water produces a suction
impelling forwards all the portions following it, is not new. It
was known to the ancient Romans and was even used in some
cases among them as a fraud, in fact as a means of cheating the
Water Commissioners of those days ; the water which could flow
through a pipe of a certain size being first agreed to be paid for and a
trumpet pipe being afterwards added to produce an increased flow.

32 PAPERS RELATING TO MOTION OF FLUIDS [8

The effect of the trumpet pipe will be readily understood
by considering that, when the pipe is flowing full of water or free
from air, the velocity of the water must diminish just as the
sectional area of the pipe increases. But the water, on account of
its inertia, tends to retain the velocity it has, and, as no air can
enter the pipe, the water tends to dash forwards leaving a vacuum
behind it; but, as the pressure of the external air prevents this,
instead of the vacuum being formed the suction is produced
tending to draw forwards the water which is behind. The very
powerful suction which the widening pipe is capable of producing,
is strikingly exemplified in some of the experiments which I have
made with the jet pump, and in which a force of suction has been
produced to the extent of 1^ times the height of the fall, thus
causing the water to flow through the jet with the velocity due to
2J times its real fall.

Having now explained the construction of the Simple Jet
Pump and the leading principles on which its action depends,
I proceed to show how a number of jet pumps can be so combined
as to form an advantageous machine adapted for the drainage of

swampy lands.

*******

For the purpose of determining the efficiency of the jet pump
under various circumstances of height of fall and of lift, with
especial reference to obtaining data for ascertaining what amount
of work can be performed in the raising of water in any of the
particular cases in which the employment of the machine may be
contemplated, I, some time since, constructed and tried the ex-
perimental apparatus represented in this drawing [shown to the
Meeting].

These results which I obtained with this apparatus I brought
before the Mechanical Section of the British Association in a
second communication made to it, at the Meeting at Hull in
1853*: but I did not then divulge the principle of the combi-
nation of jet pumps which now forms the principal object of my
communication to you.

I have now said enough to explain the applicability of the jet
pump to drainage and also to indicate the natural circumstances
requisite for its employment. It remains to consider the com-
parative merits of this and of other systems for effecting the same
* [See supra, p. 27.]

1855] ON THE JET PUMP 33

objects. It may naturally be asked, if a fall of water be available,
why not apply it to drive a common water-wheel or a turbine,
either of which might be made to raise the water by common
pumps, by centrifugal pumps, or by the ordinary scoop wheels at
present much used in the drainage of lands in Holland ?

There is no doubt that the efficiency, in respect to economy of
the water power, of the machines I have just named could readily
be made to surpass in many cases that attainable by the jet pump.
There are however numerous practical advantages connected with
the jet pump which will commonly be of greater consequence than
any slight saving of the water ; and this more particularly in cases
in which the stream supplies more power than is required for the
drainage of the swamp.

In the first place the first cost of the system of jet pumps is
greatly less than that of any other kind of machinery capable of
applying the power of the fall for raising the drainage water.
This is a very important advantage, because the cost of any kind
of water-wheels with pumping machinery is such as to prove
a serious obstacle to their employment. Next the cost due to
wear and tear in the jet pump is practically nothing : as there are
no moving parts in the machine, the motion being confined entirely
to the water itself; and the most important parts of the machine
may be made of copper so that they may be free from liability to
corrosion. In the jet pump in particular there are no valves liable
to stick or leak : no pistons requiring to be packed or to have
leathering renewed. In fact the jet pump is capable of working
on from week to week or even from year to year without requiring
to be touched for any kind of adjustment or repair. The entire
skilled labour and superintendence required for any system of
water-wheels and lifting machinery is saved by the jet pump, and
no additional labour is required in other respects for the working
of the jet pump beyond what is equally necessary for the other
kinds of machinery. The labour actually required is chiefly that
of keeping the water courses and banks in order, and of cleansing
the gratings or strainers which must be used for the removal
of sticks and other floating bodies from the water. This work is
of a kind that can be performed by the ordinary agricultural
labourers required for the cultivation of the swamp when drained.
Lastly it is to be particularly observed that while the power of
water is peculiarly well suited for raising the water from low

T. 3

34 PAPERS RELATING TO MOTION OF FLUIDS [10

lands because the same wet weather which causes an increase of
the quantity of water to be raised supplies also an increased power
for the performance of the work : the combination of jet pumps
in a series affords a remarkably simple self acting arrangement for
increasing the power of the working apparatus just in proportion
as the available power and the work to be performed are increased.

9. ON A NEW APPLICATION OF THE JET PUMP BY STEAM
AS AUXILIARY TO A LARGE DRAINAGE CENTRIFUGAL

[Read before the Belfast Natural History and Philosophical Society,
December 21, 1864. No report is preserved except the manuscript of
this introduction to the paper.]

IN the early days of attempts at railway locomotion the
puffing of the steam off directly from a waste steam pipe was
found to be noisy and annoying and to cause danger by frightening
horses. In order to mitigate these evils, it was thought advisable
to throw the waste steam into the chimney from whence it might
pass off into the air with less violence in its puffs. Soon however
an astonishing result followed on the introduction of this new
arrangement. An engine was found to be greatly improved in its
power and speed, the fire being at the same time observed to burn
much more briskly and the steam being generated more quickly.
This simple chance proved to be, more perhaps than any other
single event, or than any of the contrivances designed with high
efforts of ingenuity and skill, the turning point to success in the
railway system. The improvement in the engine referred to was
found to be due to the end of the pipe throwing the steam into
the chimney having happened to be directed upwards. The steam
blown upwards with force, and entangling itself with the smoke,
dashed the smoke forwards along with itself, and so caused a great
rush of air through the fire to the lower part of the chimney
where the partial void was thus produced. The jet blast in the
chimney has ever since been universally adopted in railway engines
as an essential stimulant to their energetic action.

Many years ago, on my having occasion to wish for a simple
means for raising water from pits beside which other water

1855] MEASUREMENT OF WATER BY WEIR-BOARDS 35

happened to be in store at higher levels, it occurred to me that
the principle used in the locomotive steam engine chimney might
be applied to effect the desired object. Following up this idea
and seeking to apply it to the best advantage under the new
proposed circumstances, I was led to combine with it some other
known hydraulic principles and so arrived at the simple and
effective apparatus which I call the Jet Pump.

10. ON PRACTICAL DETAILS OF THE MEASUREMENT
OF RUNNING WATER BY WEIR-BOARDS.

[From a manuscript abstract prepared by the Author, having
been read at the British Association, Glasgow, 1855.]

MR THOMSON did not profess in this paper to enter into the
reasoning and experiments by which formulae and tables have
been made out for ascertaining the quantity of water which flows
over a weir-board or through a notch in a vertical plate when the
width is known and the depth from the water level to the
horizontal edge of the board is observed. These reasonings and
experiments had been already discussed more or less fully in many
treatises, and very elaborately in some. Among the most accurate
and refined experiments hitherto made for providing data for use
in special cases he instanced those of MM. Poncelet and Lesbros,
carried out at Metz, in the years 1827 and 1828, and detailed in a
Memoire read at the Academy of Sciences in November 1829. His
object in the present paper for the British Association was to give
explanations of the practical arrangements which in the course of
his experience in the measurement of water by this method he
had found most convenient, of niceties to be attended to for the
attainment of accurate observations, of difficulties to be overcome,
and of errors to be avoided which he knew were very frequently
fallen into and often led to serious results.

He exhibited detailed drawings of gauging weirs which he had
used. He stated as some of the chief matters to be attended to :

(1) That the weir-board, which dams back the water and in
which the rectangular horizontal notch is cut, should present a flat
vertical surface for contact with the water, and the upper surface

3—2

36 PAPERS RELATING TO MOTION OF FLUIDS [11

of the bottom of the notch should be bevelled off in such a way
that the water may part at once from the edge of the flat vertical
face, as if it were flowing from a perfectly thin plate instead of
a board which for strength requires thickness.

(2) The pool or pond of water dammed back should be so
deep that the water may lie nearly at rest in it with a level
surface.

(3) The water should issue free from the edge of the board
with air below the falling stream.

11. ON EXPERIMENTS ON THE MEASUREMENT OF WATER
BY TRIANGULAR NOTCHES IN WEIR-BOARDS.

[From the Report of the British Association, Leeds, 1858 ; pp. 181—185.]

THE experiments proposed to be comprehended in the investi-
gations to which the present interim Report relates, have for
their object to determine the suitableness of triangular (or
V-shaped) notches in vertical plates for the gauging of running
water, instead of the rectangular notches in ordinary use. The
ordinary rectangular notches, accurately experimented on as they
have been, at great cost and with high scientific skill, in various
countries, with the view of determining the necessary formulas
and coefficients, for their application in practice, are for many
purposes suitable and convenient. They are, however, but ill
adapted for the measurement of very variable quantities of water,
such as commonly occur to the engineer to be gauged in rivers
and streams. If the rectangular notch is to be made wide
enough to allow the water to pass in flood times, it must be so
wide, that for long periods in moderately dry weather, the water
flows so shallow over its crest that its indications cannot be relied
on. To remove, in some degree, this objection, gauges for rivers
or streams are sometimes formed in the best engineering practice,
with a small rectangular notch cut down [at one end of the crest]
below the general level of the crest of a large rectangular notch.
If, now, instead of one depression being made for dry-weather use,
in a crest wide enough for use in floods, we conceive of a large
number of depressions extending so as to give to the crest the

1858] MEASUREMENT OF WATER BY V-NOTCHES 37

appearance of a set of steps of stairs, and if we conceive the
number of such steps to become infinitely great, we are led at
once to the conception of the triangular, instead of the rectangular
notch. The principle of the triangular notch being thus arrived
at, it becomes evident that there is no necessity for having one
side of the notch vertical and the other slanting; but that, as
may in many cases prove more convenient, both sides may be
made slanting, and their slopes may be alike. It is then to be
observed, that by the use of the triangular notch with proper
formulas and coefficients derivable by due union of theory and
experiments, quantities of running water, from the smallest to the
greatest, may be accurately gauged by their flow through the same
notch. The reason of this is obvious, from considering that in the
triangular notch, when the quantity flowing is very small, the flow
is confined to a small space admitting of accurate measurement ;
and that the space for the flow of water increases as the quantity
to be measured increases, but still continues such as to admit of
accurate measurement.

Further, the ordinary rectangular notch, when applied for the
gauging of rivers, is subject to a serious objection from the difficulty,
or impossibility, of properly taking into account the influence of the
bottom of the river on the flow of the water to the notch. If it were
practicable to dam up the river so deep that the water would flow
through the notch as if coming from a reservoir of still water, the
difficulty would not arise. This, however, can seldom be done in
practice; and although the bottom of the river may be so far below
the crest as to produce but little effect on the flow of the water
when the quantity flowing is small, yet when the quantity becomes
great, the " Velocity of Approach " comes to have a very material
influence on the flow of the water, but an influence which it
is usually difficult, if not impracticable, to ascertain with satis-
factory accuracy. In the notches now proposed, of triangular
form, the influence of the bottom may be rendered definite, and
such as to affect alike (or at least by some law that may be readily
determined by experiments) the flow of the water when very
small, or when very great, in the same notch. The method by
which I propose that this may be effected, consists in carrying out
a floor starting exactly from the vertex of the notch, and extending
both up stream and laterally so as to form a bottom to the channel
of approach, which will both be smooth, and will serve as the

38 PAPERS RELATING TO MOTION OF FLUIDS [11

lower bounding surface of a passage of approach unchanging in
form while increasing in magnitude at the places at least which
are adjacent to the vertex of the notch. The floor may either be
perfectly level, or may consist of two planes whose intersection
would start from the vertex of the notch, and, as seen in plan,
would pass up stream perpendicularly to the direction of the weir
board, the two planes slanting upwards from their intersection
more gently than the sides of the notch. The level floor, although
theoretically not quite so perfect as the floor of two planes, would
probably, for most practical purposes, prove the more convenient
arrangement. With reference to the use of the floor, jt may
be said, in short, that by a due arrangement of the notch and the
floor, a discharge orifice and channel of approach may be produced,
of which (the upper surface of the water being considered as the
top of the channel and orifice) the form will be unchanged or but
little changed, with variations of the quantity flowing; — very
much less certainly than is the case with rectangular notches.

The laws regulating the quantities of water flowing in such
orifices as have now been described, come naturally next to be
considered. Without, however, in the present interim Report,
attempting to enter on a detailed discussion of theoretical con-
siderations on this subject, I shall here merely advert briefly to
the principal results and methods of reasoning.

By theory I have been led to anticipate that the quantity
flowing in a given notch should be proportional, or very nearly so,
to the f power of the lineal dimensions of the cross section of the
issuing jet, or to the f power of the head of water over the vertex
of the notch. This head is to be understood, in the case of water
flowing from a still reservoir, as being measured vertically from
the level of the water surface down to the vertex of the notch ;
or, in the case of water flowing to the notch, with a considerable
velocity of approach over a floor arranged as above prescribed, the
head is to be considered as being measured vertically from the
water surface where the motion is nearly stopped by the weir
board, at a place near the board, but as far as may be found
practicable from the centre of the notch. The law here enunciated,
to the effect that the quantity flowing should be proportional to
the | power of the head, I consider should hold good rigidly in
reference to water flowing by a triangular notch in a thin vertical
plate from a large and deep reservoir of still water, if the water

1858] MEASUEEMENT OF WATER BY V-NOTCHES 39

were a perfect fluid, free from viscidity and friction, and free from
capillary attraction at its surface, and from any other slight
disturbing causes that may have minute influences on the flow,
the flow being supposed to be that due simply to gravitation
resisted by the inertia of the fluid. The like may be said of
water flowing from triangular notches with shallow channels of
approach, having floors as described above, when due attention is
given to make the passages of approach so as really to remain
unchanged in form for a sufficient distance from the notch, while
increasing in magnitude as the flow increases (such being supposed,
according to my theory, to be possible); and if due attention
be paid to measuring the heads in all cases in positions similarly
situated with reference to the varying dimensions of the issuing
streams.

In illustration of these statements, or suppositions, I would
merely say that if two triangular notches, similar in form, have
water flowing in them at different depths but with similar
passages of approach, the cross sections of the two jets at the
notches may be similarly divided into the same number of elements
of area ; and that the areas of the corresponding elements will be
proportional to the squares of the lineal dimensions of the cross
sections, or, as from various considerations may readily be assumed,
proportional to the squares of the heads ; also the velocities of the
water in the corresponding elements may be taken as proportional
to the square roots of the lineal dimensions, or to the square roots
of the heads. From these considerations, supported by numerous
others, it appears that the quantities flowing should be proportional
to the products of the squares of the heads into their square roots,
or to the | powers, as already stated.

The friction of the fluid on the solid bounding surfaces of the
passages of approach where the water moves rapidly adjacent to
the notch, may readily be assumed, from all previous experience in
similar subjects, not to have a very important influence even on
the absolute amount of the flow of the water ; and if we assume
(as is known to be nearly the case for high velocities, such as occur
in notches used for practical purposes, unless unusually small)
that the tangential force of friction of the fluid, per unit of area
of surface flowed along, is proportional to the square of the velocity
of flow, it follows by theory that the friction, although slightly
influencing the absolute amount of the flow, will not, according to

40 PAPERS RELATING TO MOTION OF FLUIDS [11

that assumption, at all interfere with its proportionality to the
| power of the head, and this condition will very nearly hold good
if the assumption is very nearly correct.

How closely the theory thus briefly sketched may be found
to agree with the actual flow of water will be a subject for
experimental investigation; and whatever may be the result in
this respect, the main object must be to obtain, for a moderate
number of triangular notches of different forms, and both with
and without floors at the passage of approach, the necessary
coefficients for the various forms of notches and approaches
selected, and for various depths in any one of them, so as to
allow of water being gauged for practical purposes, when in future
convenient, by means of similarly-formed notches and approaches.
The utility of the proposed system of gauging, it is to be
particularly observed, will not depend on a perfectly close agree-
ment of the theory described with the experiments, because in
respect to any given form of notch and approach, a table of
experimental coefficients for various depths, or an empirical formula
slightly modified from the theoretical one, will serve all purposes.
To one evident simplification in the proposed system of gauging,
as compared with that by rectangular notches, I would here advert,
namely, that in the proposed system, when once the form of the
notch and channel of approach is fixed for gauging any set of
streams, the quantity flowing comes to be treated as a function of
only one variable, namely, the measured head of water ; while in
the rectangular notches it is practically treated as a function of
at least two variables, namely, the head of water and the horizontal
width of the notch ; because in practice it would be inconvenient,
if not impossible, to select any single width of notch, or any
moderate number of widths of notches, for general use, for very
varied quantities of water. It is commonly also a function of
a third variable, very difficult to be taken into account, namely,
the depth from the crest of the notch down to the bottom of the
channel of approach ; which depth must vary in its influence with
all the varying ratios between it and the other two quantities of
which the flow is a function.

The proposed system of gauging also gives facilities for taking
another element into account which often arises in practice;
namely, the influence of back water on the flow of the water
in the gauge, when, as frequently occurs in rivers, it is found

1858] MEASUREMENT OF WATER BY V-NOTCHES 41

impracticable to dam the river up sufficiently to give it a clear
overfall, free from the back or tail water. For any given ratio of
the height of the tail water above the vertex of the notch, to the
height of the head water above the vertex of the notch, I would
anticipate that the quantities flowing would still be; approximately
at least, proportional to the f power of the head as before ; and
a set of coefficients would have to be determined experimentally
for different ratios of the height of the head water to the height
of the tail water above the vertex of the notch.

With the aid of the grant placed at my disposal by the
Association at last year's meeting, for the purposes of these
researches, I have got an experimental apparatus constructed and
fitted up at a place a few miles distant from Belfast, in Carr's
Glen, on the grounds of Mr Neeson, who has kindly afforded me
all the necessary facilities regarding the water supply and the site
for the experiments ; and I have got some preliminary experiments
made on a right-angled notch in a vertical plane surface, the sides
of the notch making angles of 45° with the horizon, and the flow
being from a deep and wide pool of quiet water, and the water
thus approaching the notch uninfluenced by any floor or bottom.
The principal set of experiments as yet made were on quantities
of water varying from about 2 to 10 cubic feet per minute ; and
the depths or heads of water varied from 2 to 4 inches in the
right-angled notch. From these experiments I derive the formula
Q = '3l"7H^, where Q is the quantity of water in cubic feet per
minute, and H the head as measured, vertically, in inches, from
the still water level of the pool, down to the vertex of the notch.
This formula is submitted, at present temporarily, as being
accurate enough for use for ordinary practical purposes for the
measurement of water by notches similar to the one experimented
on, and for quantities of water limited to nearly the same range
as those in the experiments; but as being, of course, subject
to amendment by more perfect experiments extending through
a wider range of quantities of water.

Out of the grant of £10 from the Association for these
experiments, the amount for which I have hitherto had to apply
to the Treasurer as having been expended in them is £8. Os. 4>d. ;
which leaves a balance remaining of £1. 19s. Sd.

It will be readily observed, that the experimental investigations
indicated in the foregoing report as desirable, are such as would

42 PAPERS RELATING TO MOTION OF FLUIDS [12

require for their completion, and extension to large flows of water,
a great expenditure both of time and money, like as has already
been the case with researches on the flow of water in rectangular
notches. All that I can myself for the present propose to attempt,
is to open up the subject with experiments on moderately small
flows of water ; and with this view, I would be glad to be aided,
by a further grant from the Association, in continuing experiments
of the kinds already undertaken.

12. ON EXPERIMENTS ON THE GAUGING OF WATER
BY TRIANGULAR NOTCHES.

[From the Report of the British Association, Manchester, 1861 ;
pp. 151—158.]

IN 1858 I presented to the Association an interim Report on
the new method which I had proposed for the gauging of flowing
water by triangular (or V-shaped) notches, in vertical plates,
instead of the rectangular notches, with level bottom and upright
sides, in ordinary use. I there pointed out that the ordinary
rectangular notches, although for many purposes suitable and
convenient, are but ill adapted for the measurement of very
variable quantities of water, such as commonly occur to the
engineer to be gauged in rivers and streams ; because, if the
rectangular notch be made wide enough to allow the water to
pass through it in flood times, it must be so wide that for long
periods, in moderately dry weather, the water flows so shallow
over its crest, that its indications cannot be relied on. I showed
that this objection would be removed by the employment of
triangular notches, because, in them, when the quantity flowing is
small, the flow is confined to a narrow and shallow space, admitting
of accurate measurement ; and as the quantity flowing increases,
the width and depth of the space occupied in the notch increase
both in the same ratio, and the space remains of the same form
as before, though increased in magnitude. I proposed that in
cases in which it might not be convenient to form a deep pool of
quiet water at the up-stream side of the weir-board, the bottom of
the channel of approach, when the triangular notch is used, may

1861] MEASUREMENT OF WATER BY V-NOTCHES 43

be formed as a level floor, starting exactly from the vertex of the
notch, and extending both up stream and laterally so far as that
the water entering on it at its margin may be practically considered
as still water, of which the height of the surface above the vertex
of the notch may be measured in order to determine the quantity
flowing. I indicated theoretic considerations which led to the
anticipation that in the triangular notch, both without and with
the floor, the quantity flowing would be proportional, or very
nearly so, to the f power of the height of the still-water surface
above the vertex of the notch. As the result of moderately accu-
rate experiments which I had at that time been able to make on
the flow in a right-angled notch, without floor, I gave the formula
Q = 0*317^^ where Q is the quantity of water in cubic feet per
minute, and H the head of water, as measured vertically, in
inches, from the still-water level of the pool down to the vertex
of the notch. This formula I submitted at that time temporarily,
as being accurate enough for use for many ordinary practical
purposes for the measurement of water by notches similar to the
one experimented on, and for quantities of water limited to nearly
the same range as those in the experiments (from about two to
ten cubic feet per minute), but as being subject to amendment by
future experiments which might be of greater accuracy, and might
extend over a wider range of quantities of water.

Having been requested by the General Committee of the
Association to continue my experiments on this subject, with
a grant placed at my disposal for the purpose, I have, in the
course of last summer and of the present summer, devoted much
time to the carrying out of more extended and more accurate
experiments. The results which I have now obtained are highly
satisfactory. I am confident of their being very accurate. I find
them to be in close accordance with the law which had been
indicated by theoretical considerations; and I am satisfied that
the new system of gauging, now by these experiments made
completely ready for general application, will prove to be of
great practical utility, and will afford, for a large class of cases,
important advantages over the ordinary method — for such cases,
especially, as the very varying flows of rivers and streams.

The experiments were made in the open air, in a field adjacent
to a corn-mill belonging to Mr Henry Neeson, in Carr's Glen, near
Belfast. The water-supply was obtained from the course leading

44

PAPERS RELATING TO MOTION OF FLUIDS

Waterltvel

[12

to the water-wheel of the mill, and means were arranged to allow
of a regulated supply, variable at pleasure, being drawn from that
course to flow into a pond, in one side of which the weir-board
with the experimental notch was inserted. The inflowing stream
was so screened from the part of the pond next the gauge-notch,
as to prevent any sensible agitation being propagated from it to
the notch, or to the place where the water level
was measured. For measuring the water level,
a vertical slide-wand of wood was used, with
the bottom end cut to the form of a hook (as
shown in the marginal figure), the point of
which was a small level surface of about one-
eighth of an inch square. This point of the
hook, by being brought up to the surface of the
water from below, gave a very accurate means
for determining the water level, or its rise or
fall, which could be read off by an index mark
near the top of the wand, sliding in contact
with the edge of a scale of inches on a fixed
framing which carried the wand.

By other experimenters a sharp-pointed hook, like a fishing-
hook, has sometimes, especially of late, been used for the same
purpose, and such a hook affords very accurate indications. The
result of my experience, however, leads me to incline to prefer
something larger than the sharp-pointed hook, and capable of
producing an effect on the water surface more easily seen than
that of a sharp-pointed hook ; and on the whole I would recommend
a level line like a knife-edge, which might be from one-eighth to
half an inch long, in preference either to a blunt point with level
top or a sharp point. The blunt point which I used was so small,
however, as to suit very perfectly. If the point be too large,
it holds the water up too much on its top as the water in the pond
descends, and makes too deep a pit in the surface as the water
ascends and begins to flow over it. The knife-edge would be free
from this kind of action, and would, I conceive, serve every
purpose, perfectly, except when the water has a sensible velocity
of flow past the hook, and in that case, perhaps, the sharp point,
like that of a fishing-hook, might be best.

To afford the means for keeping the water surface during
an ex eriment exactly at a constant level, as indicated by the

1861] MEASUREMENT OF WATER BY V-NOTCHES 45

point of the wooden hook, a small outlet waste- sluice was fitted
in the weir-board. The quantity of water admitted to the pond
was always adjusted so as to be slightly in excess of that required
to maintain the water level in the pond at the height at which the
hook was fixed for that experiment. Then a person lying down,
so as to get a close view of the contact of the water surface with
the point of the hook, worked this little waste or regulating
sluice, so as to maintain the water level constantly coincident with
the point of the hook.

The water issuing from the experimental notch was caught in
a long trough, which conveyed it forward with slight declivity, so
as to be about seven or eight feet above the ground further down
the hill-side, where two large measuring-barrels were placed side
by side at about six feet distance apart from centre to centre.
Across and underneath the end of the long trough just mentioned,
a til ting- trough six feet long was placed, and it was connected at
its middle with the end of the long trough by a leather flexible
joint, in such a way that it would receive the whole of the water
without loss, and convey it at pleasure to either of the barrels,
according as it was tilted to one side or the other.

Each barrel had a valve in the bottom, covering an aperture
six inches square, and the valve could be opened at pleasure, and
was capable of emptying the barrel very speedily. The capacity
of the two barrels jointly was about 230 gallons, and their content
up to marks fixed near the top for the purpose of the experiments
was accurately ascertained by gaugings repeated several times
with two- or four-gallon measures with narrow necks.

By tilting the small trough so as to deliver the water
alternately into the one barrel and the other, and emptying each
barrel by its valve while the other was filling, the process of
measuring the flowing water could be accurately carried on for as
long time as might be desired. With this apparatus, quantities
of water up to about 38 cubic feet per minute could be measured
with very satisfactory accuracy.

The experiments of which I have now to report the results
were made on two widths of notches in vertical plane surfaces.
The notches were accurately formed in thin sheet iron, and were
fixed so as to present next the water in the pond a plane surface,
continuous with that of the weir-board.

The one notch was right-angled, with its sides sloping at

46 PAPERS RELATING TO MOTION OF FLUIDS [12

45° with the horizon, so that its horizontal width was twice its
depth. The other notch had its sides each sloping two horizontal
to one vertical, so that its horizontal width was four times its
depth.

In each case experiments were made both on the simple notch
without a floor, and on the same notch with a level floor starting
from its vertex, and extending for a considerable distance both up
stream and laterally. The floor extended about two feet on each
side of the centre of the notch, and about two and a half feet in
the direction up stream, and this size was sufficient to allow the
water to enter on it with only a very slow motion — so slow as to
be quite unimportant. The height of the water surface^ above
the vertex of the notch was measured by the sliding hook at a
place outside the floor, where the water of the pond was deep and
still.

The principal results of the experiments on the flow of the
water in the right-angled notch without floor are briefly given in
the annexed table:

H [Ins.] Q [Cubic ft. per min.] c

1 39-69 -3061
6 26-87 -3048
5 17-07 -3053
4 9-819 -3068
3 4-780 -3067

2 1-748 -3088

the quantity of water given in column 2 for each height of 2, 3,
4, 5, 6, and 7 inches being the average obtained from numerous
experiments comprised in two series, one made in 1860, and the
other made in 1861, as a check on the former set, and with a view
to the attainment of greater certainty on one or two points of
slight doubt. The second set was quite independent of the first,
the various adjustments and gaugings being made entirely anew.
The two sets agreed very closely, and I present an average of the
two sets in the table as being probably a little more nearly true
than either of them separately. The third column contains the
values of the coefficient c, calculated for the formula Q = cH2, from
the several heights and corresponding quantities of water given in
the first and second columns, H being the height, as measured
vertically in inches from the vertex of the notch up to the still-
water surface of the pond, and Q being the corresponding quantity

1861] MEASUREMENT OF WATER BY V-NOTCHES 47

of water in cubic feet per minute, as ascertained by the experiments.
It will be observed from this table that, while the quantity of
water varies so greatly as from If cubic feet per minute to 39,
the coefficient c remains almost absolutely constant ; and thus the
theoretic anticipation that the quantity should be proportional, or
very nearly so, to the f power of the depth is fully confirmed by
experiment. The mean of these six values of c is '3064; but,
being inclined to give rather more weight, in the determination of
the coefficient as to its amount, to some of the experiments made
this year than to those of last year, I adopt '305 as the coefficient,
so that the formula for the right-angled notch without floor
will be

Q = -305#i

My experiments on the right-angled notch with the level floor,
fitted as already described, comprised the flow of water for depths
of 2, 3, 4, 5, and 6 inches. They indicate no variation in the
value of c for different depths of the water, but what may be
attributed to the slight errors of observation. The mean value
which they show for c is "308 ; and as this differs so little from
that in the formula for the same notch without the floor, and as
the difference is within the limits of the errors of observation,
and because some consecutive experiments, made without and
with the floor, indicated no change of the coefficient on the
insertion of the floor, I would say that the experiments prove
that, with the right-angled notch, the introduction of the floor
produces scarcely any increase or diminution on the quantity
flowing for any given depth, but do not show what the amount of
any such small increase or diminution may be, and I would give
the formula

Q = '305M

as sufficiently accurate for use in both cases. The experiments
in both cases were made with care, and are without doubt of
very satisfactory accuracy ; but those for the notch without
the floor are, I consider, slightly the more accurate of the two
sets.

The experiments with the notch with edges sloping two
horizontal to one vertical showed an altered feature in the flow of
the issuing vein as compared with the flow of the vein issuing
from the right-angled notch. The edges of the vein, on issuing

48 PAPERS RELATING TO MOTION OF FLUIDS [12

from the notch with slopes two to one, had a great tendency to
cling to the outside of the iron notch and weir-board, while the
portions of the vein issuing at the deeper parts of the notch
would shoot out and fall clear of the weir-board. Thus, the vein
of water assumed the appearance of a transparent bell, as of
glass, or rather of the half of a bell closed in on one side by
the weir-board and enclosing air. Some of this air was usually
carried away in bubbles by the stream at bottom, and the
remainder continued shut up by the bell of water, and existing
under slightly less than atmospheric pressure. The diminution
of pressure of the enclosed air was manifested by the sides of the
bell being drawn in towards one another, and sometirries even
drawn together, so as to collapse with one another at their edges
which clung to the outside of the weir-board. On the full
atmospheric pressure being admitted, by the insertion of a knife
into the bell of falling water, the collapsed sides would instantly
spring out again. The vein of water did not always form itself
into the bell ; and when the bell was formed, the tendency to the
withdrawal of air in bubbles was not constant, but was subject to
various casual influences. Now it evidently could not be supposed
that the formation of the bell and the diminution of the pressure
of the confined air could occur as described without producing
some irregular influences on the quantity flowing through the
notch for any particular depth of flow, and this circumstance must
detract more or less from the value of the wider notches as means
for gauging water in comparison with the right-angled notch with
edges inclined at 45° with the horizon. I therefore made numerous
experiments to determine what might be the amount of the
ordinary or of the greatest effect due to the diminution of pressure
of the air within the bell. I usually failed to meet with any
perceptible alteration in the quantity flowing due to this cause,
but sometimes the quantity seemed to be increased, by some small
fraction, such as one, or perhaps two, per cent. On the whole,
then, I do not think that this circumstance need prevent the use,
for many practical purposes, of notches of any desired width for
a given depth.

My experiments give as the formula for the notch, with slopes
of two horizontal to one vertical and without the floor,

Q = 0-636 M

1861] MEASUREMENT OF WATER BY V-NOTCHES 49

and for the same notch, with the horizontal floor at the level
of its vertex,

(2 = 0*628#2.

In all the experiments from which these formulas are derived, the
bell of falling water was kept open by the insertion of a knife or
strip of iron, so as to admit the atmospheric pressure to the
interior. The quantity flowing at various depths was not far from
being proportional to the f power of the depth, but it appeared
that the coefficient in the formula increased slightly for very small
depths, such as 1 or 2 inches. For instance, in the notch with
slopes 2 to 1 without the floor, the coefficient for the depth of
2 inches came out experimentally 0*649, instead of 0*636, which
appeared to be very correctly its amount for 4 inches depth. It
is possible that the deviation from proportionality to the f power
of the depth, which in this notch has appeared to be greater than
in the right-angled notch, may be due partly to small errors in the
experiments on this notch, and partly to the clinging of the falling
vein of water to the outside of the notch, which would evidently
produce a much greater proportionate effect on the very small
flows than on great flows. The special purpose for which the
wide notches have been proposed is to serve for the measurement
of wide rivers or streams in cases in which it would be inconvenient
or impracticable to dam them up deep enough to effect their flow
through a right-angled notch. In such cases I would now further
propose that, instead of a single wide notch, two, three, or more
right-angled notches might be formed side by side in the same
weir-board, with their vertices at the same level, as shown in the
annexed figure. In cases in which this method may be selected,

the persons using it, or making comparisons of gaugings obtained
by it, will have the satisfaction of being concerned with only
a single standard form of gauge-notch throughout the investigation
in which they may be engaged.

T. 4

50 PAPERS RELATING TO MOTION OF FLUIDS [12

By comparison of the formulas given above for the flows
through the two notches experimented on, of which one is twice
as wide for a given depth as the other, it will be seen that in the
formula for the wider notch the coefficient "636 is rather more
than double the coefficient '305 in the other. This indicates that
as the width of a notch, considered as variable, increases from that
of a right-angled notch upwards, the quantity of water flowing
increases somewhat more rapidly than the width of the notch for
a given depth. Now, it is to be observed that the contraction of
the stream issuing from an orifice open above in a vertical plate is
of two distinct kinds at different parts round the surface of the
vein. One of these kinds is the contraction at the place's where
the water shoots off from the edges of the plate. The curved
surface of the fluid leaving the plate is necessarily tangential with
the surface of the plate along which the water has been flowing,
as a» infinite force would be required to divert any moving particle
suddenly out of its previous course *. The other kind of contraction
in orifices open above consists in the sinking of the upper surface,
which begins gradually within the pond or reservoir, and continues
after the water has passed the orifice. These two contractions
come into play in very different degrees, according as the notch
(whether triangular, rectangular, or with curved edges) is made
deep and narrow, or wide and shallow. From considerations of
the kind here briefly touched upon, I would not be disposed to
expect theoretically that the coefficient c for the formula for
V-shaped notches should be at all truly proportional to the
horizontal width of the orifice for a given depth ; and the experi-
mental results last referred to are in accordance with this
supposition. I would, however, think that, from the experimental
determination now arrived at, of the coefficient for a notch so
wide as four times its depth, we might very safely, or without
danger of falling into important error, pass on to notches wider
in any degree, by simply increasing the coefficient in the same
ratio as the width of the notch for a given depth is increased.

* This condition appears not to have been generally noticed by experimenters
and writers on hydrodynamics. Even MM. Poncelet and Lesbros, in their de-
lineations of the forms of veins of water issuing from orifices in thin plates, after
elaborate measurements of those forms, represent the surface of the fluid as making
a sharp angle with the plate in leaving its edge.

1861] MEASUREMENT OF WATER BY V-NOTCHES 51

APPENDIX — April, 1862.

With reference to the comparison made, in the concluding
sentences of the foregoing Report, between the quantities of water
which, for any given depth of flow, are discharged by notches
of different widths, and to the opinion there expressed, that we
might, without danger of falling into important error, pass from
the experimental determination of the coefficient for a notch so
wide as four times its depth, to the employment of notches wider
in any degree, by simply increasing the coefficient in the same
ratio as the width of the notch for a given depth is increased,
I now wish to add an investigation since made, which confirms
that opinion, and extends the determination of the discharge
beyond the notches experimented on, to notches of any widths
great in proportion to their depths. This investigation is founded
on the formula for the flow of water in rectangular notches
obtained from elaborate and careful experiments made on a very
large scale by Mr James B. Francis, in his capacity as engineer
to the Water-power Corporation at Lowell, Massachusetts, and
described in a work by him, entitled Lowell Hydraulic Experi-
ments, Boston, 1855*. That formula, for either the case in
which there are no end-contractions of the vein, or for that in
which the length of the weir is great in proportion to the depth
of the water over its crest, and the flow over a portion of its
length not extending to either end is alone considered, is

i ........................ (1),

where L^ — length of the weir over which the water flows, without
end-contractions ; or length of any part of the weir not extending
to the ends, in feet : Hl = height of the surface-level of the
impounded water, measured vertically from the crest of the weir,
in feet : and Ql = discharge in cubic feet per second over the length
Ll of the weir.

It is to be understood that, in cases to which this formula
is applicable, the weir has a vertical face on the upstream side,
terminating at top in a level crest ; and the water, on leaving the
crest, is discharged through the air, as if the weir were a vertical
thin plate.

To apply this to the case of a very wide triangular notch : —

* The formula is to be found at page 133 of that work.

4—2

52 PAPERS RELATING TO MOTION OF FLUIDS [12

Let ABC be the crest of the notch, and AC the water level in the
impounded pool. Let the slopes of the crest be each m horizontal
to 1 vertical: or, what is the same, let the cotangent of the

inclination of each side of the crest to the horizon be = m. Let

/y»

AE, a variable length, = as. Then ED = — . Let EG be an

m

infinitely small element of the horizontal length or width from A
to C. Then EG may be denoted by dx. Let q = quantityMn cubic
feet per second flowing under the length x, that is, under AE in
the figure. Then dq will be the quantity discharged per second
between ED and GF.

Then, by the Lowell formula just cited, we have

m
whence, by integrating, we get

g -8-38(1)*. | «l + 0,

\ml 5

in which the constant quantity is to be put = 0, because when
x = 0, q also = 0. Hence we have

Let now H2 = height in feet from the vertex of the notch up to
the level surface of the impounded water = BK in the figure.
Then AK = mH2. Let also Q2 = the discharge per second in the
whole triangular notch = twice the quantity discharged under
AK. Then by formula (2) we get

or

Q2 = 2-664 w.#22 ..................... (3).

To bring the notation to correspond with that used in the fore-
going Report, let Q = the quantity of water in cubic feet per
minute, and H = the height of the water level above the vertex
in inches.

1861] MEASUREMENT OF WATER BY V-NOTCHES 53

O fT

Then Q2 = ~r and Hz = and by substitution in (3), we get

........................ (4).

This formula then gives, deduced from the Lowell formula, the
flow in cubic feet per minute through a very wide notch in a
vertical thin plate, when H is the height from the vertex of the
notch up to the water level, in inches, and when the slopes of the
notch are each m horizontal to 1 vertical.

As to the confidence which may be placed in this formula,
I think it clear that, for the case in which the notch is so wide,
or, what is the same, the slopes of its edges are so slight, that the
water may flow over each infinitely small element of the length
of its crest without being sensibly influenced in quantity by
lateral contraction arising from the inclination of the edges, the
formula may be relied on as having all the accuracy of the Lowell
formula from which it has been derived ; and I would suppose
that when the notch is of such width as to have slopes of about
four or five to one, or when it is of any greater width whatever,
the deviation from accuracy in consequence of lateral contraction
might safely be neglected as being practically unimportant or
inappreciable.

This formula for wide notches bears very satisfactorily a com-
parison with the formulas obtained experimentally for narrower
notches, as described in the foregoing Report. For slopes of 1 to

1 the formula was Q = '305 H%, and for slopes of 2 to 1 the formula

was Q = '6'36H*. To compare these with the one now deduced
for any very slight slopes, we may express them thus :
For slopes of 1 to 1

and for slopes of 2 to 1

while for any very slight slopes, or for any very wide notches,
the formula now deduced from the Lowell one is

The very slight increase from '318 to '320 here shown in
passing from the experimental formula for notches with slopes
of 2 to 1, to notches wider in any degree — that slight change,

54 PAPERS RELATING TO MOTION OF FLUIDS [13

too, being in the right direction, as is indicated by the increase
from *305 to '318 in passing from slopes of 1 to 1, to slopes of
2 to 1 — gives a verification of the concluding remarks in the
foregoing Report ; and this may serve to induce confidence in the
application in practice of the formula now offered for wide
notches.

[If two cases of liquid flow through orifices or channels are
compared, in the second of which all distances parallel to one
direction (say the axis of h) are contracted in the same^ratio as
compared with the first, it may be readily seen from the dynamical
equations that, provided the motion is steady, the paths of all the
elements of liquid, and also the pressures, will correspond in the
two cases, when the effects of viscosity and capillary attraction are
neglected. In these latter circumstances the law that the delivery
of a notch is proportional to its width will therefore be exact.
See also infra, pp. 67 seq. Dec. 1910.]

13. TABLE OF FLOW OF WATER IN THE RIGHT-ANGLED

V-NOTCH.

[The following MS. table has been found among Prof. Thomson's papers.]

ACCORDING to the formula, Q = '305/^, where Q denotes the
quantity of water in cubic feet per minute, and h denotes the
height in inches from the vertex of the notch up to the still water
surface level.

The notch may be either without floor or with floor, as the
quantities flowing in these two cases for same heights are found
experimentally to be very nearly the same.

The Formula, however, and with it the Table, is reliable for
more minute exactitude in the case of the notch without floor.

Fuller information is to be found in an Interim and Final
Report to the British Association by Prof. James Thomson
published in the Volumes of the Association for 1858 and 1861 ;

1861]

MEASUREMENT OF WATER BY V-NOTCHES

55

and in a paper by him on " The Flow of Water through Orifices "
in the Volume of the Association for 1876.

TABLE.

h Q
ins. cub. ft.
per min.

h Q
ins. cub. ft.
per min.

h Q
ins. cub. ft.
per min.

h Q
ins. cub. ft.
per min.

| -054

5J 19-26

9£ 93-5

19 480

g -094

5| 20-43

10 96-4

191 496

| -148

5| 21-64

10J 102-6

W 512

•218

of 22-89

lOl 109-0

19} 529

1 -305

5| 24-18

10} - 115-6

20 546

1| -409

5$ 25-52

11 122-4

20i 580

1| -533

6 26-89

11£ 129-5

21 616

If -676

6i 28-33

11^ 136-8

211 654

l| -840

6| 29-79

11| 144-4

22 692

If 1-027

6f 31-29

12 152-1

221 732

If 1-23

6l 32-85

12| 160-2

23 774

If 1-47

6f 34-46

121 168-5

23| 817

2 1-73

6f 36-10

12| 177-0

24 861

21 2-01

6| 37-80

13 185-8

25 953

2| 2-32

7 39-54

13| 194-9

26 1051

2f 2-66

7| 41-33

13^ 204-2

27 1155

2| 3-01

7j 43-17

13| 213-8

28 1265

2f 3-41

7f 45-05

14 223-7

29 1381

2| 3-82

7i 46-98

14£ 233-8

30 1504

2| 4-27

7| 48-97

14| 244-2

31 1632

3 4-75

7| 51-0

14| 254-8

32 1767

3| 5-27

7| 53-1

15 265-8

33 1908

3| 5-81

8" 55-2

15| 277-0

34 2056

3f 6-38

8£ 57-4

15i 288-5

35 2210

3| 6-99

8| 59-6

15} 300-3

36 2372

3f 7-63

8f 61-9

16 312-3

37 2540

3| 8-30

8| 64-2

16J 324-7

38 2715

3f 9-01

8§ 66-6

16i 337-3

39 2897

4 9-76

8f 69-1

16} 350-2

40 3086

4i 10-54

8| 71-6

17 363-4

41 3283

4£ 11-35

9 74-1

171 376-9

42 3487

4| 12-21

91 76-7

17* ' 390-8

43 3698

4j 13-10

9f 79-4

17| 404-9

44 3917

4§ 14-03

9| 82-1

18 419

45 4143

4| 14-99

9| 84-8

181 434

46 4377

4£ 16-00

9f 87-7

18* 449

47 4619

5 17-05

9| 90-5

18| 464

48 4869

5£ 18-13

i

56 PAPERS RELATING TO MOTION OF FLUIDS [14

14. IMPROVED INVESTIGATIONS ON THE FLOW OF WATER
THROUGH ORIFICES WITH OBJECTIONS TO THE MODES OF
TREATMENT COMMONLY ADOPTED.

[From the Report of the British Association, Glasgow, 1876, pp. 243—266.]

THE methods usually put forward for treating of the flow of
water out of vessels by orifices in thin plates, slightly varied
though they may be in different cases, are ordinarily founded on
assumptions largely alike in these different cases, and largely
erroneous. The theoretical views so arrived at, and very generally
promulgated, are in reality only utterly false theories based on
suppositions of the flow of the water taking place in ways which
are kinematically and dynamically impossible, and are at variance
with observed facts of the flow, and even at variance with the
facts as put forward by the advancers themselves of those theories.
The admittedly erroneous results brought out through those
fallacious "theories," and commonly miscalled "theoretical results"
are afterwards considerably amended by the introduction into the
formulas so obtained of constant or variable coefficients, or other-
wise, so as to be brought into some tolerable agreement with
experimental results. These means of practical amendment,
however, being themselves not established on any scientific
principles, can at best only conduce to the attainment of useful
empirical formulas, but cannot, by their application to the
originally false theoretical views, come to develop any true
scientific theory. A theory may, no doubt, be regarded as a good
scientific theory, and as being good for practical purposes, which
leaves out of account some minor features or conditions of the
actual facts. In so far as it leaves any influential elements out
of account, it is imperfect; but if the conditions which, for
simplicity, or from want of complete knowledge of the subject,
or for any other reason, are left out, be of very slight influence
on the practical results in question, the theory may be regarded
as a very good one, though not quite perfect. In the case,
however, of the hydraulic theories now referred to, the false
principles involved in the reasonings relate to the main and
important conditions of the flow, and not to any mere minor

1876]

ON THE FLOW OF WATER THROUGH ORIFICES

considerations, the imperfections or errors of which might be of
but slight importance in the development of the main principles
involved, and but little influential on the results sought to be
attained.

I will now proceed to give some examples or sketches of the
usual methods of treating the subject.

I will first take the case of water flowing from a state of rest
through an orifice in a vertical plane face. This case is ordinarily
treated by supposing the orifice to be divided into an infinite
number of infinitely narrow horizontal bands of area, and supposing
the velocity of the water in each band to be that due, through
the action of gravity, to a fall from the still-water surface-level
down to that band ; then multiplying that velocity by the area
of the band, and treating the product as being the volume flowing
per unit of time across that horizontal band or element of the
area; and integrating to find the sum of all these volumes of
water for all the bands, and treating this sum as being the
"theoretical" volume per unit of time flowing across the whole
area of the orifice. This result is commonly called the "theoretical
discharge" per unit of time ; but, as it is known not to be the
actual discharge, it is then multiplied by a numerical coefficient
called by some "the coefficient of contraction" and by others the
"coefficient of discharge" in order to find the actual discharge per
unit of time.

Thus for the case of a rectangular orifice in a vertical plane
face, as in fig. 1 — where WL is the level of the still-water surface,

Fig. 2.

and ABCD is the orifice, with two edges AB and CD level, and
EF is an infinitely narrow horizontal band extending across the
orifice at a depth h below the still-water surface-level, and having
dh as its breadth vertically measured, while it has I, the horizontal
length of the orifice, as its length, and where, as shown in the

58 PAPERS RELATING TO MOTION OF FLUIDS [14

figure, the depths of the top and bottom of the orifice below WL
are denoted by h± and h2 respectively — if q is put to denote the
so-called "theoretical" volume per unit of time, and Q the actual
volume per unit of time, it is commonly stated that

dq = J%gh . Idh,
whence q = f * Jtyh .ldh = l J%g P" tidh,

J hi J hi

or q =

and then when c is put to denote the so-called "coefficient of
contraction,'1 it is stated that the actual quantity flowing ner unit
of time is

-h) .......... . .......... (1).

It is then customary to deduce from this a formula for the
case of water flowing in a rectangular notch open above, as in
fig. 2, by taking /^ = 0, and so deriving, for the open notch, the
formula

Qf or notch = %dj2~g.h% .................. (2).

These examples may suffice for indicating the nature of the
method commonly advanced ; and it may be understood that the
same method with the necessary adaptations is usually given for
finding the flow through circular orifices, triangular orifices, or
orifices of any varied forms whatever.

Now this method is pervaded by false conceptions, and is
thoroughly unscientific.

First. Throughout the horizontal extent of each infinitely
narrow band of the area the motion of the water has not the same
velocity, and has not the same direction at different parts ; and
the assumption of the velocity being the same throughout,
together with the assumption tacitly implied of the direction of
the motion being the same throughout, vitiates the reasoning
very importantly. It is thus to be noticed at the outset that the
division of the orifice into bands, infinitely narrow in height, but
extending horizontally across the entire orifice, cannot lead to a
satisfactory process of reasoning, and that the elements of the
area to be separately considered ought to be infinitely small both
in length and in breadth.

Secondly. For any element of the area of the orifice infinitely
small in length and breadth it is not the velocity of the water at

1876] ON THE FLOW OF WATER THROUGH ORIFICES 59

it that ought to be multiplied by the area of the element to find
the volume flowing per unit of time across that element, but it is
only that the velocity's component which is normal to the plane
of the element that ought to be so multiplied.

Thirdly. Whether, for any element of the area of the orifice,
we wish to treat of the absolute velocity of the water there, or to
treat of the component of that velocity normal to the plane of
the orifice, it is a great mistake to suppose that the velocity at
the element is that due by gravity to a fall from the still- water
surface-level of the pent-up statical water down to the element.
The water throughout the area of any closed orifice in a plane
surface, with the exception of that flowing in the elements situated
immediately along the boundary of the orifice, has more than
atmospheric pressure; and hence it can be proved* that it must
have less velocity than that due to the fall from the still- water
surface-level down to the element.

The foregoing may be illustrated by consideration of the very
simple case of water flowing from a vessel through a rectangular
orifice in a vertical plane face, two sides of the rectangle being
level, and the other two vertical, and end contractions being
prevented by the insertion of two parallel guide walls or plane
faces, one at each end of the orifice, and both extending some
distance into the vessel perpendicularly to the plane of the orifice,
so that the jet of issuing water may be regarded as if it were a
portion of the flow through an orifice infinitely long in its hori-
zontal dimensions.

Thus if the jet shown in section in fig. 3 a be of the kind here
referred to, while WL is the still-water surface-level, the so-called
"theoretical velocities" at the various depths in the orifice, which
are dealt with as if they were in directions normal to the plane
of the orifice, can be, and very commonly are, represented hy the
ordinates of a parabola as is shown in fig. 3 6, where ED represents
in magnitude and direction the "theoretical velocity" at the top
of the orifice, CE the "theoretical velocity" at the bottom of the
orifice, and FG that at the level of any point F in the orifice —
these ordinates being each made =*J%gh, where h is the depth
from the still-water surface down to the level of the point in the
orifice to which the ordinate belongs. Then, under the same
mode of thought, or same set of assumptions, the area of that
* Theorem I., further on [p. 64], will afford proof of this.

60

PAPERS RELATING TO MOTION OF FLUIDS

[14

parabola between the upper and lower ordinates (BD and GE)
will represent what is commonly taken as the "theoretical discharge''
per unit of time through a unit of horizontal length of the orifice.
But this gives an excessively untrue representation of the actual
conditions of the flow. Instead of the parabola, some other curve,
very different, such as the inner curve sketched in the same
diagram, fig. 3 b, but whose exact form is unknown, would, by its
ordinates, represent the velocity-components normal to the plane

w

Fig. 3.

36

of the orifice for the various levels in the orifice, and its area
would represent the real discharge in units of volume per unit
of time through a unit of horizontal length of the orifice. Although
the exact form of this true curve is unknown, yet we may observe
that it must have its ordinates each less than the ordinate for the
same level in the parabola.

The truth of this may be perceived through considerations
such as the following. First, it is to be noticed that for the very
top and the very bottom of the orifice, instead of the ordinates
BD and CE of the parabola, the ordinates of the true curve must

1876] ON THE FLOW OF WATER THROUGH ORIFICES 61

be each zero ; because, at each of these two places, the direction
of the motion is necessarily tangential to the plane of the orifice*,
and so the velocity-component normal to the plane of the orifice
must be zero ; and that component, not the velocity itself, is what
the ordinate of the true curve must represent. On the hypothesis
of perfect fluidity in the water (which, throughout the present
discussions and investigations, is assumed as being a close enough
representation of the truth to form a basis for very good theoretical
views), the velocities at top and bottom of the orifice will be those
due by gravity to falls from the still-water surface-level down to
the top and bottom of the orifice respectively, because at these
places the water issues really into contact with the atmosphere,
and consequently attains atmospheric pressure. At all intervening

* The assertion here made, to the effect that the directions of the stream-lines
which form the external surface of the jet on its leaving the edge of the orifice
must, at the edge, be tangential to the plane of the orifice when the orifice is in a
plane face, or must in general be tangential to the marginal narrow band or
terminal lip of the internal or water-confining face of the plate or nozzle in which
the orifice is formed, can be clearly and easily proved, although, strangely, the
fact has been and is still very commonly overlooked. Even MM. Poncelet and
Lesbros, in their delineations of the forms of veins of water issuing from orifices
in thin plates, after elaborate observations and measurements of those forms, re-
present the surface of the issuing fluid as making a sharp angle with the plane
wetted face in leaving the edge ("Experiences Hydrauliques sur les Lois de
1'Ecoulement de 1'Eau," a Memoir read at the Academy of Sciences in November
1829, and published in the Memoires, Sciences Mathematiques et Physiques,
tome in.). Other writers on Hydraulics put forward very commonly repre-
sentations likewise erroneous. Weisbach, for instance, in his valuable works
(Ingenieur und Maschinen-Mechanik, Vol. i. § 313, fig. 427, date 1846; and
Lehrbuch der theoretischen Mechanik, 5th ed., date 1875, edited by Hermann,
§ 433, fig. 772), has assumed (not casually, but with deliberate care, and after
experimental measurements made by himself), as the best representation which,
with available knowledge of the laws of contraction of jets of water, can be given
for the form of the contracting vein of water issuing from a circular orifice in a
thin plate, a solid of revolution specified clearly in such a way that the water
surface in leaving the plane of the plate makes an angle of about 67° with that
plane, and states to the effect that that water surface is just a continuation of the
paths of the stream-lines within the vessel which he represents at the margin of
the orifice as crossing the plane of the orifice with converging paths making the
angle already mentioned of about 67° with that plane. They ought in reality to
leave the lip tangentially to the plane, and then to make a very rapid turn in a
short space (or to have a very small radius of curvature) on just leaving the lip
of the orifice. The prevalence of erroneous representations and notions on this
subject was adverted to, and an amendment was adduced, by myself in a Report to
the British Association in 1861 on the Gauging of Water by V-Notches (Brit. Assoc.
Eep. Manchester Meeting, 1861, Part 1, p. 156). [See supra, p. 42.]

62 PAPERS RELATING TO MOTION OF FLUIDS [14

points in the plane of the orifice it may readily be seen, or may
with great confidence be admitted, that the pressure will be in
excess of the atmospheric pressure ; because, neglecting for sim-
plicity the slight and, for the present purpose, unimportant
modification of the courses of the stream-lines caused by the force
of gravity acting directly on the particles composing the stream-
lines, as compared with the courses which the stream-lines would
take if the action of gravity were removed, and the water were
pressed through the orifice merely by pressure applied, as by a
piston or otherwise, to the fluid in the vessel, we may say, truly
enough for the present purpose, that an excess of pressure at the
convex side of any stream -line is required in order that the* water
in the stream-line can be made to take its curved path. The
mode of reasoning on this point suggested here may be obvious
enough, although, for the sake of brevity, it is here not completely
expressed. It follows that at all these intervening points in the
plane of the orifice the absolute velocity of the water will be less
than that due to a fall from the still-water surface down to the
level of the point in the orifice ; and besides, at all depths in the
plane of the orifice except a single medial one, the direction of
the flow will be oblique, not normal, to the plane of the orifice.
Hence, further, through these two circumstances, jointly or
separately as the case may be, it follows obviously that the
ordinates of the true curve will everywhere be less than those of
the parabola.

Fig. 4 illustrates in like manner the false theoretical and the
true actual conditions of the flow over a level upper edge of a
vertical plane face, which may be exemplified by the case of a
rectangular notch without end contractions, or of a portion of the
flow not extending to either end in a very wide rectangular notch.
In this case it is to be observed that the ordinates at and near
the top of the issuing water in the vertical plane of the orifice
must be only slightly less than those of the parabola — because,
at the very top or outside of the stream, atmospheric pressure is
maintained throughout the length of any stream-line, and so the
velocity will be very exactly that due by gravity to the vertical
depth of the flowing particle below the still-water surface-level
in the vessel ; and because, also, the direction of the motion does
not deviate much from perpendicularity to the plane of the
orifice. Lower down in the plane of the orifice the direction of

1876]

ON THE FLOW OF WATER THROUGH ORIFICES

63

the water's motion will approach still more nearly to being
perpendicular to that plane ; but there the pressure will be
considerably in excess of the atmospheric pressure, and so the
velocity will be considerably less than that due by gravity to a
fall through the vertical distance from the still-water surface-
level down to the stream-line in the plane of the orifice. At
places still further down in the orifice the flow comes to be
obliquely upwards ; and this obliquity is so great as to render
the normal component very much less than the actual velocity,
while the actual velocity itself is less than that due by gravity
to the depth of the particle below the still-water surface-level.
At this region of the flow then, for both reasons, the ordinates
of the true curve are less than those of the parabola. Lastly,

4a

Fig. 4.

4&

at the very bottom of the orifice, or immediately over the top of
the crest of the notch, the water issues into contact with the
atmosphere, and so attains to atmospheric pressure, and must
therefore have the velocity due by gravity to its depth below
the still-water surface-level. Here, however, its direction of flow
is necessarily tangential to the plane face of the vessel from
which it is shooting away, and consequently is vertically
upwards. Hence the normal component of its motion is zero,
and so the ordinate of the true curve at that place is zero in
length, instead of the normal component being greater at the
bottom of the orifice than at any higher level, and instead of
that component being properly represented by the ordinate there
of the parabola.

64 PAPERS RELATING TO MOTION OF FLUIDS [14

Like explanations to those already given might be offered for
other forms of orifices (for circular or triangular orifices or V-
notches, and for orifices in general which may be in vertical or
horizontal or inclined plane faces, or in faces of other superficial
forms than the plane), and it might be shown that in general
the ordinary modes of treating the subject are very faulty.

The examples already discussed may suffice to direct attention
to the faulty character of the ordinarily advanced theories, and
to give some suggestions of directions in which reforms are
requisite.

I will now proceed to offer some improved investigations
which are applicable to many of the most ordinary and most
useful cases in practical hydraulics, in reference to the flow of
water through orifices in thin plates, or from the wetted internal
surface of vessels terminating abruptly in orifices. In devising
and arranging these investigations I have aimed at putting them
in such form as that they may be intelligible and completely
demonstrative to students even in the early stages of their progress
in dynamical studies.

Definition. The free level for any particle of water in a mass
of statical or of flowing water is the level of the atmospheric end
of a column, or of any bar straight or curved, of particles of statical
water, having one end situated at the level of the particle, and
having at that end the same pressure as the particle has, and
having the other end consisting of a level surface of water freely
exposed to the atmosphere, or else having otherwise atmospheric
pressure there ; or briefly we may say that the free level for any
particle of water is the level of the atmospheric end of its pressure-
column, or of an equivalent ideal pressure-column.

THEOREM I. In the case of steady flow from approximate rest
of water or any liquid considered as frictionless and incompressible,
the velocity of any particle in the stream is equal to the velocity
which a body would receive in falling freely from rest through a
vertical space equal to the fall of free level which is incurred by the
particle in the stream during its flow from rest to its existing position.

Or, in briefer words sufficiently suggestive, it may be said
that, in respect to water or any liquid flowing so as to admit of
its being regarded as truly enough frictionless and incompressible,
In steady flow, the velocity generated from rest is that due by
gravity to the fall of free level.

1876]

ON THE FLOW OF WATER THROUGH ORIFICES

65

Or if f be the fall of free-level sustained by any particle in
passing from a statical region of the mass of water to a point in
the region of flow, and if v be the velocity of the particle when at
that point, then

In fig. 5, let WL be the still-water surface-level, and let B'BB"
be a bounding interface separating the region of flow with
important energy of motion from the region which may be
regarded as statical, or as devoid of important energy of motion.
Let U'UU" be another interface crossing the stream-lines at any
place in the region of flow.

Fig. 5.

Now taking as the unit of volume the cube of the unit of
length, taking as the unit of area the square of the unit of length,
taking the unit of density as unit of mass per unit of volume, so
that the density of a body will be the number of units of mass
per unit of volume, taking as the unit of force the force which
acting on a unit of mass for a unit of time imparts to it a unit
of velocity (that is to say, using the unit of force selected according
to the system of Gauss, and which is often called the "absolute"
or the "kinetic" unit of force*), and taking water-pressures as
being reckoned from the atmospheric pressure as zero, let

* The units of force derivable by the method of Gauss from the various units of
length, mass, and time, in common use, though spoken of under general designa-
tions such as " absolute units of force " or " kinetic units of force" have until lately
T. 5

66 PAPEKS RELATING TO MOTION OF FLUIDS [14

p = density of the water ;
v = velocity at U ;

Jib = pressure-height at B, or the height of a column of statical
water which would produce the pressure at B ;

h = pressure-height at U ;

pb = pressure in units of force per unit of area at B ;
p = pressure in units of force per unit of area at U ;
/= fall from B to U, measured vertically ;

f = fall of free level in the flow from the region of statical

water to U\

then pi = gplii ,

and p = gph.

Let a small mass, m, of the water, whose volume (or content
voluminally considered) is denoted by c, be introduced into the
stream, its first place being at B just outside of the initial interface
B'BB", and let it flow forward in the stream till it reaches a
second place at U where it is just past the interface U'UU". In
the stream filament BUE the space between the two interfaces
at B and U is traversed alike by both front and rear of the small
mass m ; and therefore no excess of energy is given or taken by
the mass in consequence of the pressure on its front and of that
on its rear, for the passage of its front from the interface at B to
that at U, and of its rear over the same space.

been individually anonymous : and this deficiency, notwithstanding the important
scientific and practical uses which these units were capable of serving, has been a
great hindrance and discouragement to their general employment in dynamical
investigations, and even to any satisfactory spread of knowledge of their meaning.
Three years ago, the British- Association Committee on Dynamical and Electrical
Units (Brit. Assoc. Report, 1873, Part 1, p. 222), taking the centimetre, the gram,
and the second as units of length, mass, and time, named the force so derived the
Dyne. For the unit of force derived from the foot, the pound, and the second,
the name Poundal has been introduced by myself ; and it seems likely to come into
use. At this Meeting of the British Association I have proposed the Crinal and
the Funal as names for the two units of force derived respectively, one from the
decimetre, the kilogram, and the second, and the other from the metre, the tonne,
and the second [see Paper reprinted infra, "On Metric Units of Force, Energy,
and Power, larger than those on the Centimetre-Gram-Second System."] The
familiarization of these important units to the minds of students of dynamics
will, in a very important degree, aid the acquisition of clear and true views in
hydrokinetics, as also in dynamics generally.

1876] ON THE FLOW OF WATER THROUGH ORIFICES 67

But work given to it by pressure from behind, while it is
passing the initial interface at B, is

= pb.c
= gphb.c;

or that work is

since pc — m.

Again, during the emergence of the mass past the interface at
U, it gives away to the water in front of it a quantity of work
which, in like manner, is

= p .c

= gph.c

— gmh.

Also during the passage of the particle from its first place
at B to its place at U it descends a vertical space =/; hence
during that passage it receives from gravity a quantity of work

On the whole the mass receives an excess of work beyond
what it gives, and that excess of work received is

= gmhb + gmf— gmh
= gm(hb+f-h)

and as this is the work taken into store as kinetic energy, we
have to put it = ^mv2. That is,

or v

which is the result that was to be proved in Theorem I.

THEOREM II. ON THE FLOW OF WATER THROUGH ORIFICES

SIMILAR IN FORM AND SIMILARLY SITUATED RELATIVELY TO THE

STILL- WATER SURF ACE- LEVEL. In the flowing of water, from
the condition of approximate rest, through orifices similar in form
and similarly situated relatively to the still-water surface-level*,
the stream-lines in the different flows are similar in form : also
the velocity of the water at homologous places is proportional to the

* Or free level of the still water.

5—2

68 PAPERS RELATING TO MOTION OF FLUIDS [14

square root of any homologous linear dimension in the different
flows: and also (pressures being reckoned from the atmospheric
pressure as zero) the pressure of the water on homologous small
interfaces in the different flows is proportional to the cube of any
homologous linear dimension ; or, in other words, the fluid pressure
(super-atmospheric), per unit of area (it homologous places, is
proportional to any homologous linear dimension.

Preparatively for the demonstration of this theorem, it is
convenient to establish some dynamic principles, which, for
present purposes, may be regarded as lemmas or preparatory
propositions, and which will be grouped here together under the
single heading of Proposition A.

PROPOSITION A. If there be two or more vessels containing
water pent up in an approximately statical condition, and if they
have similar orifices similarly situated relatively to the free level of
the statical water — and if we imagine the water to be guided in
each case to and onward past the orifice by an infinite number of
infinitely small frictionless guide-tubes arranged side by side, like
the cells of a honeycomb, and having their walls or septums* of no
thickness — and if, in the different vessels, these guide-tubes be, one
set to another, similar in form, though they may be of quite
different forms from the forms which the stream-lines would them-
selves assume if the floius were unguided — and if, at the homologous
terminations of the guide-tubes, fluid pressures be anyhow main-
tained proportional, per homologous areas, to the cube of any
homologous linear dimension, or, what is the same, if pressures be
maintained proportional, per unit of area, to the homologous linear
dimension, — then the velocity of the water at homologous places
will be proportional to the square root of the homologous linear
dimension, and the pressure of the water at homologous places on
homologous areas will be proportional to the cube of the homologous
linear dimension ; and the water will press, at homologous places,
on homologous areas of the septums, with a force on one side in
excess of that on the other, which will be proportional to the cube
of the homologous linear dimension.

NOTE. For brevity in what follows, pressures at homologous
places on homologous areas will be called homologous pressures,
and pressures per unit of area will be called unital pressures]

* The English form for the plural of septum, when septum is used as an English
word, is here purposely preferred to the Latin septa.

1876] ON THE FLOW OF WATER THROUGH ORIFICES 69

and any difference of the fluid pressures on the opposite sides of
any small portion or element of a septum will be called a
differential pressure.

The demonstration of the proposition will be aided by first
noticing the following relation in respect to two small solid
masses in motion. If two similar small solid bodies of masses m
and m', having their homologous linear dimensions as 1 to n, are
guided to move along similar curves, having likewise their homo-
logous linear dimensions as 1 to n (fig. 6), and if the velocities
of the bodies at homologous points in their paths be as 1 to *Jn,
then —

First. Their gravities are as 1 to ri\ evidently.

Second. Their "centrifugal forces"* applied by them in the
plane of curvature and normally to the guide are also as 1
to ns.

Fig. 6. Fig. 7.

Let r and r' be put to denote the radii of curvature of the
paths at homologous places. Then centrifugal forces are as

mv

* The name "centrifugal force" is here adopted in the sense in which it is
commonly used. I fully agree with the opinion now sometimes strongly urged to
the effect that this name is not a very happily chosen one ; for two reasons : —
first, because the name centrifugal would be better applied to a motion o: flying
from the centre, than to a force acting outwards along the radius ; and secondly,
because the body really receives no outward force, no force in the direction from
the centre, but receives a centreward force which, being unbalanced, acts against
the inertia of the body, and diverts the body from the straight line of its instanta-
neous motion. The centreward force actually received by the body, and which is
the force acting on it normal to its path, may be called the deviative force received
by the body. This is equal and opposite to the outward force called "centrifugal
force," which is not received by the body, but is exerted outwards by it against
whatever is compelling it to deviate from the straight line of its instantaneous
motion. The name " centrifugal force," however, although objected to, is in too
general use throughout the world to allow of its immediate abandonment.

70 PAPERS RELATING TO MOTION OF FLUIDS [14

But m' = nsm,

v' = Jn . v,
r' = nr.
Hence the centrifugal forces are

mv2 n3m.nv'*
as — : — - ,
r nr

or as 1 : w3.

This being understood, it readily becomes evident that if,
instead of small solid masses sliding along guides, we Jiave two
small homologous masses of water m and m, fig. 7, flowing in
similar slender guide-tubes, and if homologous pressures be applied
to the two masses in front and behind, which are as 1 to n3, and
if at homologous situations in their two paths their velocities be
as 1 to Jnt then, in respect to all the forces received by the two
masses from without, other than those applied by the guide-
tubes, and also in respect to the forces required to be received
for counteracting their centrifugal forces, we see that all these
constitute force systems similar in arrangement and of amounts
as 1 to n3. It therefore follows that the forces which the masses
must receive from their guide-tubes must be similarly arranged
and of amounts, on homologous small areas, as 1 to n3.

This being settled, we may now pass to the demonstration of
Proposition A, at present in question.

Suppose No. 1 and No. 2 in fig. 8 to represent two similar
vessels with similarly guided flows, in all respects as described in
the enunciation of this proposition. Let WL and W'L' be the
still-water surface-levels, or the free levels of the still water in the
two cases. Let BCD, B'C'D' be two similar bounding interfaces,
each separating the region of flow with important energy of
motion from the region which may be regarded as statical, or as
devoid of important energy of motion. Let BUE in No. 1 and
B'U'E' in No. 2 be two homologous guide-tubes, and let them for
the present be understood as terminating at two homologous
cross interfaces E and E', which may conveniently be understood
as being each situated at a moderate distance outside of the orifice
—for instance, at some such place as that which is usually spoken
of as being the "vena contracta," or where the water has attained
a pressure not differing much from that of the atmosphere, or it

1876]

ON THE FLOW OF WATER THROUGH ORIFICES

71

may in some cases even be that the atmospheric pressure is there
attained; but the exact places at which to suppose the homologous
terminations E and E' of the two guide-tubes as being taken are
not at all essential to the demonstration.

Let homologous linear dimensions in No. 1 and No. 2 be as
1 to n.

Let the velocity at any variable point U in the guide-tube
SUE be denoted by v.

Let the pressure at Ut expressed in units of pressure-height,
be denoted by A; as shown by the vertical line UT in No. 1, where
T is the top of the pressure-column for the point U.

No. 1.

Fig. 8.

No. 2.

Let the pressure at B, the beginning of the tube, on the
initial interface, outside of which the water may be regarded as
statical, or as having no important energy of motion, be denoted
by hb ; or, what comes to the same thing, let the depth from the
still-water surface-level down to the beginning of the tube at B
be denoted by hb, as is marked in the figure. It is thus to be
noticed that the fall of free level incurred by a particle in flowing
along the guide-tube from B to U is the vertical distance from the
still- water surface-level, WL, down to T, the top of the pressure-
column for the flowing water at U. This fall of free level may be
denoted (in conformity with the notation in Theorem I) by f,

72 PAPERS RELATING TO MOTION OF FLUIDS [14

Let the vertical descent from B to U be denoted by f\ so
that/ is the fall of a particle in passing from B to U. In case
of an ascent in any guide-tube, from its beginning to any point U
in its course, we shall have the fall /"negative.

Let the abatement of pressure-height from B to U be denoted
by k, or let hb — h = k. Thus in case of an increase of pressure-
height in any guide-tube, from its beginning to any point U in its
course, k will be negative.

For No. 2, let the same letters of reference to the diagram,
and the same notation, be used as for No. 1, with the modification
for No. 2 merely of the attachment of an accent to each letter.

Now as a part of the data on which the present investigation
under Proposition A is founded, it is to be assumed that a unital
pressure is somehow maintained at JE', the end of the guide-tube
in No. 2, n times that which is anyhow maintained at the cor-
responding point E in No. 1. Thus, if we denote these two
pressures expressed as pressure-heights, at E and Er respectively,
by he and (he)f, we have (he)' = nhe ; and hence the fall of free
level from beginning to end in No. 2 is n times the fall of free
level from beginning to end in No. 1.

Hence putting ve and (ve)' to denote the velocities at E and E'
respectively, we have (by Theorem I, which proves that the
velocities must be proportional to the square roots of the falls of
free level)

or (ve)' = ven .............................. (1).

Again, from similarity of forms, we have in respect to areas of
cross-sections of the two guide-tubes : —

area at E area at E'

area at U area at V '
or since reciprocals of equals are equal : —

velocity at E velocity at E'
velocity at U velocity at U' '

* = W

V V

or v' = vjn ........................... (2).

1876] ON THE FLOW OF WATER THROUGH ORIFICES 73

This applies to any or all homologous points in the two regions of
flow.

Now by referring to the figure or otherwise, it will readily be
seen that f, or the fall of free level from B to £7, is = hb +/— h,
while k = hb-h; and that therefore ?=/+ k. Hence, by Theorem
I, we have

In like manner in No. 2 : —

but by (2) v' = Jn. v.

Hence

or f' + k' = nf+ nk.

But by similarity of forms

/=«/•

Hence, subtracting equals from equals, we have

k' = nk ........................... (3);

but by similarity of forms

(hb)' = nhb ........................... (4).

Also, since the pressure at any point in a stream-line, or guide-
tube, is its initial pressure minus the relief of pressure, we have

hb-k = h ........................... (5)

and (hb)'-kf = hf ........................... (6).

From this last by (4) and (3) we get

nht — nk^li, or n (hb — k) = ti \
whence by (5)

h' = nh ........................... (7).

From this, if we put P and P' to denote total pressures on homo-
logous small areas at U and U', it follows that

P'=n*P ........................... (8).

This holds good for any homologous places in any homologous
guide-tubes, and so it holds for immediately adjacent places in
any two contiguous guide-tubes. Hence, in respect to any small
element of the septum between two adjacent guided stream-
filaments in Flow No. 1, considered comparatively with a

74 PAPERS RELATING TO MOTION OF FLUIDS [14

homologous element of a septum in Flow No. 2, the homologous
differential pressures in No. 1 and No. 2 will be as 1 to n3.

Thus the demonstration is now completed of all that is
included in Proposition A; and we are ready to go forward to
the demonstration of Theorem II, for which Proposition A was
meant to be preparative. For this we have to observe that the
conclusions arrived at in Proposition A hold good, no matter
what may be the forms of the guide-tubes, provided that they
be similar in both flows ; and no matter what may be the dis-
tribution of pressures throughout a terminal interface crossing
the assemblage of guide- tubes in No. 1, provided that the
homologous pressures throughout a homologous terminal interface
in No. 2 be anyhow maintained severally n3 times those in No. 1.
Hence, if in Flow No. 1 the guide-tubes be formed so that the
water shall flow along exactly the same paths as if it were left
unguided, and were left free to shoot away, past the interface at
E, to a distance from the orifice great in proportion to the thick-
ness of the issuing stream, without meeting any obstruction—
and if the guide-tubes in No. 2 be similar to them — and if in
No. 1 the system of pressures distributed throughout the terminal
interface at E be made exactly the same as if the water were
flowing freely for a great distance past that terminal interface —
and if in No. 2 the system of homologous distributed pressures
throughout a homologous terminal interface at E' be anyhow
maintained severally ns times those in No. 1, — it follows that the
differential pressure on the two sides of any element of a septum
in Flow No. 1 will be zero, as the guide-tubes have there no duty
to perform. Then, on the homologous septum element in No. 2,
the differential pressure, being ns times that in No. 1, will be zero
also. Hence in No. 2 the guide-tubes have no duty to perform,
and the water flows in them exactly as if it were left unguided,
but had still throughout its terminal interface the stated system
of distributed pressures somehow applied.

Now, for completing the demonstration of Theorem II, nothing
remains needed except to show that this stated system of dis-
tributed pressures requisite to be applied throughout the
terminal interface at E' will very exactly be applied on that
interface backwards by the water in front of it, which constitutes,
for the time being, the continuation of the stream past that
interface.

1876]

ON THE FLOW OF WATER THROUGH ORIFICES

75

For proof of this, conceive any cross interface FF (fig. 9),
further forward in No. 1 than EE is, and conceive a similarly
situated cross interface F'F' in No. 2. By exactly the same mode
of reasoning as before (making use of the like supposed introduction
and subsequent removal of guide-tubes), that reasoning being now
applied to the two flows commencing at the initial interfaces
BCD and B'C'D', and continued to the terminal interfaces FF
and F'F', it results that if the jet in No. 1 be allowed to flow
freely to and far past the interface FF, the jet in No. 2 terminating
at F'F' can be left to flow unguided, with stream-lines similar
to those in No. 1, and with the same relations of pressures and

No. 1.

Fig. 9.

No. 2.

velocities at its various places to the pressures and velocities in
No. 1 as have been already proved for the flow terminating at
E'E', provided that homologous pressures n3 times those at FF
be anyhow maintained at F'F'. Thus, then, we see that if
adjusted or requisite pressure systems, such as have been already
fully explained, be maintained at FF and F'F', the two streams,
one extending backward from FF to EE, and the other from F'F'
to E'E', will transfer backward just such pressures to successive
places in retrograde order in their courses as that they will of
themselves apply, at the interfaces EE and E'E', exactly the
already specified requisite pressure systems. Thus we can depart

76 PAPERS RELATING TO MOTION OF FLUIDS [14

as far as we please from the orifices forward along the two streams
to the places where, for purposes of reasoning, certain definite
pressures are to be supposed to be applied in two homologous
cross interfaces. Now it may be taken as evident that, by going
far enough away from the orifice to the terminal cross interface,
we can make, for any disturbances or departures from the specified
pressure relations, the effects propagated backwards to the water
in and near the orifices as small as we please ; or that, even if we
were to apply not exactly the strictly requisite pressure systems
at those terminal places, still the effects of this departure from
perfect exactitude would fade away rapidly in either stream as
we transfer the place under consideration backwards against the
current towards the orifice. In corroboration of this, observation
on the flow of water spouting from an orifice may be appealed to
as setting this matter beyond doubt, through its showing that
any changes of pressure introduced in a jet of water at any place
far away from the orifice (as, for instance, by the insertion of a
rigid obstruction) will transmit scarcely the slightest effect back
to the region of the orifice; or, in other words, that in a free-
flowing jet spouting through the air, the effects of obstructions
fade away rapidly in the direction contrary to the current, so as
to become imperceptible at a very moderate distance taken back
from the obstacle in the direction against the flow — very moderate
relatively to the thickness of the jet.

Even without this appeal to experimental observation, we
might almost intuitively perceive, or might readily admit, that
the introduction of more or less pressure than any stated amount
in the stream, at a place where it has got well clear of the orifice,
would be only very slightly influential on the flow as to pressures
and as to velocities and directions of motion within the vessel
and near the orifice and contracting vein. A reason for this is,
that while an obstruction in a free jet will require a great change
in mode of flow of the jet close in front of it, yet the jet
approaching to that region need have its outer filaments turned
aside only very slightly indeed to allow of all parts moving forward
without any of their stream-lines, whether medial or at or near
the surface, being subjected to almost any increase of pressure,
and consequently without the velocities of any of them being
almost at all retarded. This will readily be clearly understood
by reference to fig. 10, where the water is shown as spouting

1876] ON THE FLOW OF WATER THROUGH ORIFICES 77

against a stone without being made to thicken its stream sensibly
in consequence of the obstruction, except for a very short distance
at G in front of the stone — that is to say, in the back-stream
direction from the stone. If we were to suppose that the stone
would have a tendency to produce, at such a place as K, any
considerable increase of pressure in the internal or central stream-
filaments of the jet, we would have to notice that the external
stream-filaments next the atmosphere would fail to resist this
augmented pressure ; and, instead, they would, with only a very
slight change in their own velocities or pressures, yield a little
outwards, and so would not exert on the internal filaments the
confining action that would be requisite for the maintaining of
more than an extremely slight augmentation of pressure in those
internal filaments. Then it is obvious that if the pressure is

Fig. 10.

very little augmented, the velocity must be very little abated ;
and so, for this reason, the stream will not tend to thicken itself
except very slightly, because any considerable increase of cross-
sectional area of the stream would require an important abate-
ment of velocity, which, as said before, would require a great
increase of pressure in the internal filaments, while the external
filaments would fail to exert that necessary confining pressure.
These external filaments could, with very little change in their
own velocities, allow even of a great augmentation of the cross-
sectional area of the jet if the internal filaments, by abated velocity,
were requiring to become considerably thicker than before, in
virtue of the introduction of the obstruction. It is only the
rapid change of direction of motion of the particles of water in
the outer filaments in the neighbourhood of G, close to the

78 PAPERS RELATING TO MOTION OF FLUIDS [14

obstruction, that enables them, by what may be called their
centrifugal force, to maintain a greatly increased internal pressure
very close to the obstruction, and so to allow of the water in the
internal stream-filaments abating its velocity, and of those filaments
themselves swelling in their transverse dimensions.

These considerations complete all that is necessary for the
demonstration of Theorem II, and it may now be regarded as
proved.

FORMULA FOR THE FLOW OF WATER IN THE V-NOTCH.

From the foregoing principle we can find intuitively the
formula for the quantity of water which will flow through a
V-notch in a vertical plane surface, as in fig. 11. We can see it
at once by considering any stream-filament in the flow in one

Fig. 11.

notch, and the homologous stream-filament in the similar flow in
another notch similarly formed, but having its vertex at a different
depth below the still-water surface-level. Let the ratio of the
depth of the vertex of the one notch below the still-water surface-
level to the depth of the vertex of the other be as 1 to n, so that
all homologous linear dimensions in the two flows will be likewise
as 1 to n. Then, in passing from any cross section of one of the
two homologous filaments to the homologous cross section of the
other, we have the cross-sectional area x ft2, and the velocity of
flow oc 'Jn ; and the volume of water flowing per unit of time,
being as the cross-sectional area and the velocity conjointly, will
vary as we pass from the one to the other of the pair of homo-
logous filaments, so as to be oc n? V/i. Then, as this holds for
every pair of homologous stream-filaments throughout the two
flows, if we put Q to denote the quantity, reckoned voluminally,

1876] ON THE FLOW OF WATER THROUGH ORIFICES 79

flowing per unit of time in each of the two entire flows, we
have

Q oc n*.

Now, as well as considering two separate notches with different
streams flowing in them at the same time, we may, when it suits
our purpose, consider one single notch with streams of different
depths flowing at different times ; and if in various cases, either
of the same V-notch or of different but similar V-notches, we
denote the height of the still-water surface-level above the level
of the vertex of the notch by h, we have

Q = ch* .............................. (9),

where c is a constant coefficient, which cannot be determined by
theory, but can be very satisfactorily determined by experiment
for any desired ratio of horizontal width to vertical depth to be
adopted for the form of the notch. Experiments determining
the values of c for certain forms and arrangements of V-notches,
suited for practical convenience and utility, have already been
made by myself, and have been reported on to the British
Association ; and the Reports on them are printed in the British
Association volume for Leeds Meeting, 1858*, and in that for
Manchester Meeting, 1861 f.

INVESTIGATION OF A FORMULA FOR THE FLOW OF WATER IN A
RECTANGULAR NOTCH WITH LEVEL CREST IN A VERTICAL
PLANE FACE.

It is to be premised that the long-known and generally used
formulas for the flow of water in rectangular notches, brought
out by the so-called "theories" which I have dissented from in the
earlier part of the present paper, have been mainly of th>' form

where Q denotes the volume per unit of time,

L denotes the horizontal length of the notch,

h the vertical height from the crest of the notch to the

still- water surface-level, and
g the coefficient for gravity,

and where c has either been taken as a constant numerical co-
efficient for want of accurate experiments to determine its values

* [Supra, p. 36.] f [Supra, p. 42.]

80 PAPERS RELATING TO MOTION OF FLUIDS [14

for different values of L and h, or has been treated as a variable.
Poncelet and Lesbros have taken this latter course, and have
deduced by experiments extensive tables of its values for different
depths of water in notches of the width on which they experi-
mented — a width, namely, of 20 centimetres*. As, however, the
coefficient for terrestrial gravity varies but little for different
parts of the world, it has most frequently been left out of account,
a single coefficient c' being used instead of eg', so that if, for
instance, when the foot and second are used as units of length
and time, we take 32'2 as a correct enough statement of the value
of g for any part of the world, we have c' — 32'2c. v

A new formula, involving an important improvement in its
form and adjusted so as to be in due accordance with numerous
elaborate experiments, was developed within or about the time
from 1846 to 1855, in America, by Mr Boy den and Mr Francis,
both of Massachusetts. It is

where Q is the quantity of water in cubic feet per second,
L is the length of the notch in feet,
h is the height from the level of the crest to the still-water

surface-level in feet, and
n is the number of end contractions, and must be either

0, 1, or 2.

This formula was offered by Mr James B. Francis, in his
work entitled Lowell Hydraulic Experiments, and published at
Boston in 1855, not as one founded on any complete theoretical
views, but as one depending on several assumptions probably not
perfectly correct, and yet as one which, through numerous trials
and by adjustments introduced tentatively in fitting it to experi-
mental results, had been brought out so as to agree very closely
with experiments.

In § 120, at page 72 of his work, Mr Francis says : — " No
correct formula for the discharge of water over weirs, founded
upon natural laws, and including the secondary effects of these
laws, being known, we must rely entirely upon experiments,
taking due care in the application of any formula deduced from
thence not to depart too far from the limits of the experiments

* Memoires de V Academic des Sciences : Sciences Mathematlques ct Physiques,
Tome m. 1829.

1876] ON THE FLOW OF WATER THROUGH ORIFICES 81

on which it is founded." And in §§ 123, 124, at page 74, in
respect to the conception of the formula, he further gives the
following very clear explanations : — " The contraction which takes
place at the ends of a weir diminishes the discharge. When the
weir is of considerable length in proportion to the depth of the
water flowing over, this diminution is evidently a constant quantity,
whatever may be the length, provided the depth is the same;
we may, therefore, assume that the end contraction effectively
diminishes the length of such weirs, by a quantity depending
only upon the depth upon the weir. It is evident that the
amount of this diminution must increase with the depth ; we are
unable, however, in the present state of science, to discover the
law of its variation ; but experiment has proved that it is very
nearly in direct proportion to the depth. As it is of great
importance, in practical applications, to have the formula as simple
as possible, it is assumed in this work (Mr Francis's book) that
the quantity to be subtracted from the absolute length of a weir
having complete contraction, to give its effective length, is directly
proportional to the depth. It is also assumed that the quantity
discharged by weirs of equal effective lengths varies according
to a constant power of the depth. There is no reason to think
that either of these assumptions is perfectly correct ; it will be
seen, however, that they lead to results agreeing very closely with
experiment.

" The formula proposed for weirs of considerable length in
proportion to the depth upon them, and having complete
contraction, is

Q=C(L-bnh)h*;

in which Q = the quantity discharged in cubic feet per second ;

C = a constant coefficient ;

L = the total length of the weir in feet ;

b = a constant coefficient ;

n = the number of end contractions. In a single weir
having complete contraction, n always equals 2 ;
and when the length of the weir is equal to the
width of the canal leading to it, n = 0;

h = the depth of water flowing over the weir taken far
enough upstream from the weir to be unaffected by
the curvature in the surface caused by the discharge;

a = a constant power."
T. 6

82 PAPERS RELATING TO MOTION OF FLUIDS [14

This formula, Mr Francis states, was first suggested to him
by Mr Boyden in 1846.

The important novel feature in this formula consists in the
subtraction which it makes, from the length L of the notch, of
a length for each end contraction directly proportional to the
height of the still-water surface-level above the crest in order to
find what may be treated in the formula as the effective length.

The formula in its general form here last noted expressed
only in symbols, as also in its subsequently developed form here
previously stated with numerical coefficients arrived at by
tentative application of numerous experiments, is thtfls to be
regarded as an ingeniously arranged and valuable empirical
formula, but not as one founded on any trustworthy hydrokinetic
theory. It is founded partly on the old ordinary false "theoretical"
views, and partly on good conjectural assumptions, and is adjusted
and approximately verified by elaborate experiments conducted
on a scale unusually large, and with unusually good means for
attainment of exact results. Mr Francis, it is to be noticed,
explains that, in the formula as finally brought out, the index
for the power of the height of the water is taken as an exact
fraction, | , in preference to some unascertained fractional expression,
different in no great degree from f , merely for the attainment of
facility in calculations in the practical applications of the formula,
and not for any theoretic reason. Also it is to be noticed, in
respect to the value ^ which he assigned for the symbol 6, that
the symbol itself was first assumed as a constant rather than some
unknown variable dependent on h, and was afterwards fixed at
the particular value ^ for the sake, in both cases, of attaining
a convenient degree of simplicity which by trials was found to be
attainable, consistently with good accordance between the repre-
sentations afforded by the formula and the results shown by
experiments. He supposed, however, that "many other values of
a and b (probably an unlimited number) might be found that
would accord somewhat nearer with the experiments*."

Many years ago, after my having become acquainted with the
empirical formula thus made out by Mr Boyden and Mr Francis,
it occurred to me as desirable to attempt to investigate by hydro-
kinetic principles, without special experiments, a true formula for

* Lowell Hydraulic Experiments, § 156, p. 118 ; § 153, p. 116 ; and the passage
quoted above from § 123, p. 74.

1876] ON THE FLOW OF WATER THROUGH ORIFICES 83

the flow of water in rectangular notches in vertical thin plates, or
vertical plane faces, on the hypothesis of the water being a perfect
or frictionless fluid, and by using in the formula symbols for
constant coefficients, which, after the finding of the formula, might
be determined by a small number of accurate experiments, and
might further be tested as to their trustworthiness, or might be
amended so as to become more exact, by a large number of varied
experiments. It will be interesting to notice that the formula
which had previously been arrived at in America by Mr Boyden
and Mr Francis in the way already described is in perfect agree-
ment with the formula which, by my own investigation, is brought
out by strict scientific principles as a highly exact formula for
water considered as a perfect fluid, and as being a very satisfactory
representation of the truth for real water.

It is to be noticed at the outset that obviously a notch may
be made so long relatively to the depth of its crest from the still-
water surface-level, that, for any additional length, the increase
of the flow will be proportional to the additional length. Let mh,
in which m is a constant multiplier, be such a length as that, for
additional length, the additional flow will be proportional to the
addition made to the length. In fig. 12 let AB be the crest of
the notch, and let CD be the level of the still-water surface of the
pent-up water. Let AE and BF be each equal to Jra/t, so that,
over the part EF of the crest there will flow a quantity of water
exactly proportional to the length of EF if the width of the notch
be varied while the depth h of the water remains unchanged.
Let the length EF be denoted by I ; then

I = L — mh.

Now, out of the entire flow, conceive the middle portion which
flows over EF, and may be regarded as bounded laterally by two
vertical planes perpendicular to the plane of the orifice, one
passing through ER and the other through FS, to be taken away ;
and suppose the two remaining parts which flow over AE and
BF, with the necessary lateral parts of the notch-plate to be
brought together as shown in fig. 13, so as to form one notch
having mh for its width and h for the height from crest to still-
water level, and in which, therefore, the width of the notch shall
bear a constant ratio to the height of the water, when the height
varies, the width being always m times the height.

6—2

84

PAPERS RELATING TO MOTION OF FLUIDS

[14

Then, by exactly the same mode of procedure as that already
used for finding a formula to show how the quantity of water
flowing in a V-notch varies with the depth of the vertex or with
any other linear dimension of the flowing stream, we can readily
see that if we put Q' to denote the volume of water flowing per
unit of time in the case represented in fig. 13, we shall have

(10),

where a is a constant coefficient.

!J™fH

Fig. 12.

Fig. 13.

Next to find an expression for the quantity (voluminally
reckoned) flowing over the middle part EF of the crest, we may
consider, first, of that middle part, a portion GK taken always of
a length bearing a constant ratio to h ; and for simplicity we may
take it of length equal to h*. Now in this stream, since the
width has in general a constant ratio to the depth, or, in the case
more particularly considered, since the width is equal to the
depth, the quantity flowing per unit of time will, as in the

* Or, to meet the case in which there might not be, between E and F, a length
so great as h, we might as well consider, in another notch having great width and
having a height of flow equal to h, a portion of the flow not near either lateral
extremity of the notch, and occupying a length of the crest equal to h.

1876] ON THE FLOW OF WATER THROUGH ORIFICES 85

preceding case, be proportional to the f power of the depth ; or
we have

Flow over GK = /3h2 VA, where (3 is constant.

Hence if q± be the flow, in units of volume per unit of time, over a
unit of length in EF, we have

ql = j3h VI

By multiplying this by I we get the quantity flowing over the
entire middle part EF per unit of time ; and so, denoting that
quantity by Q", we have

.(11).

or Q" = /3 (L — mh) h VA j

Adding the expressions for Q' and Q" together, we get for the
total flow in the whole notch, which we may denote by Q,

Q = /3 (L - mh) h<Jh + ah2 *Jht
or Q = jSLh *Jh — (ftm — a) h? VA,

or

a,\,
hjh .

But — -= — is a constant; and let it be denoted by 26; and

instead of the constant /3 we may, in order now to use English
letters, put a. Then

Q = a(L-2bh)h* ..................... (12),

which is the desired formula for the flow of water in a rectangular
notch with two end contractions.

This formula admits of easy modification to give a formula
suitable for a notch with only one end contraction *, thus : —

Let the width of the notch with only one end contraction be
denoted by L (as in fig. 14). Then conceive a notch twice as wide

* It is to be understood that contraction may be prevented at either end of a
notch by there being a vertical plane side face for the channel of approach to the
notch, that side face being perpendicular to the plane of the notch, and extending
up-stream from the notch so as to reach beyond the region of incipient rapid flow
to the notch, and extending for a little way down-stream past the notch, so as to
afford the necessary guidance to the issuing stream-filaments. In like manner, by
two parallel vertical side walls or side faces to the channel, when the crest of the
notch extends quite across from the one wall-face to the other, contraction may be
prevented at both ends.

86

PAPERS RELATING TO MOTION OF FLUIDS

[14

with two end contractions as shown in fig. 15. The flow in this
double space will, by the formula last obtained (12), be seen to
be = a (2L — 2bh) h* ; and so if we put now Q to denote the flow
in the notch under consideration (shown in fig. 14), which will
be half the flow in fig. 15, we have for the notch with only one
end contraction

Q = a(L-bh)h$ (13).

Also from (11), by changing, as done before, the letter /3 into the
English letter a, we see that for a notch with no end contraction

Fig. 14.

Fig. 15.

(contractions being prevented at both ends by vertical guiding
side faces perpendicular to the plane of the notch) we would have

(14).

Now the three formulas (12), (13), and (14) may be combined
so as to be expressed together, thus : —

Q = a(L-nbh)h* ..................... (15),

where n is the number of end contractions, and must be either
2, 1, or 0.

To determine the constants a and 6, all that would be necessary
would be to have two very accurate experiments on the flow of
water in one notch at different depths, or in two notches of the

1876] ON THE FLOW OF WATER THROUGH ORIFICES 87

same kind with the ratio of the width to the depth not the same
in both. Then, putting into the formula the measured values of
L, h, and Q for the one experiment, and then again those for the
other, we would have two equations with two unknown symbols,
and so we could find the numerical values of those symbols. It
would, of course, be desirable, for experimental verification of the
theory on which the formula is founded, as also for mutual
verification or testing of the experimental results themselves, to
have numerous experiments on the flow for various depths in
various notches of different widths, so as to find whether the
formula would fit satisfactorily to them all, or to all of them that,
after comparison, would be found trustworthy — provided that the
width of the notch be not too small in proportion to the depth of
the flow, or that in all cases the width be sufficient to allow of
there being at least some small part in the middle where the rate
of flow per unit of time would be proportional to the length of
the part of the crest to which that flow would belong.

Mr Francis's experiments and his reductions of the results
carried out in his own way give the formula complete, with its
numerical coefficients, as follows: —

where Q = the discharge in cubic feet per second ;
L = the length of the notch in feet ;
n = the number of end contractions ;

h = the height from the crest to the still-water surface-level
in feet.

Mr Francis also states that this formula is not applicable to
cases in which the height h from the crest to the still-water
surface-level exceeds one-third of the length, nor to very small
depths. In the experiments from which it was determined the
depths varied from 7 inches to 19 inches; and he remarks that
there seems- no reason why it should not be applied with safety to
any depths between 6 inches and 24 inches.

PAPERS RELATING TO MOTION OF FLUIDS

[15

V

15. ON THE "VENA CONTRACTA*."

Extract from a letter of WILLIAM FROUDE, Esq., O.E., F.R.S., to Sir WM
THOMSON, dated Chelston Cross, Torquay, 2Qtk December, 1875.

[Read before the Philosophical Society of Glasgow, February 23, 1876.]

* * * "ONE result I have tried came out well: — the discharge
through an introverted cylinder

with keen edge. Here by theory **v f

the area of the section of the jet
ought to be exactly half that of
the aperture. For the conserva-
tion of stream line energy obliges
the velocity to be that due to the
head, while the conservation of
momentum requires that the
pressure on the aperture (which
here is the sole operative pressure
acting in the ultimate direction
of the velocity generated) is only
sufficient to create as much mo-
mentum, say, per second, as will
be resident in the length delivered
per second, of a column of dis-
charge of half the sectional area
of the aperture, if its velocity is that due to the head.

"The cylinder was quite smooth outside, and the edge quite
keen. The area ratio came out 0*503, 0*502, &c., instead of
0*500, and the little excess was obliterated, if the head was
counted, to about J the diameter of the aperture below the edge ;
as indeed it ought to be (I won't swear to the exact figure J),
because till the motion of the particles is purely parallel to the
axis, there must be some acceleration to be effected in the direction
of the axis, and this demands the employment of some vertical

pressure.

*******

* [The theory here given is due originally to Borda who verified it by experi-
ment. It was rediscovered by Hockin ; see Proc. Lond. Math. Soc. Vol. in. 1869,
p. 4, with a note added by Maxwell. Cf. Lamb, Hydrodynamics, 1906, footnote to
§24.]

1876]

ON THE " VENA CONTRACTA "

89

"In the vena contracta experiment with the thin plates and

open air between the plates, the
fluid was welcome, if it pleased, to
start tangentially from the plane
of the aperture as here indicated,
and as it appears to do if closely

studied. So also with the introverted cylinder; though it was
not possible to see what happened, I have no doubt that the

motion of the particles next the
edge was vertical upwards, the
curvature being only such as the
pressure in the contiguous stream
/ / / - e could satisfy. If the experiment
was not adroitly initiated, the
water seized the inner surfaces
of the cylinder and ran out in
an eddied condition, filling the

discharge pipe. When, however,
it was properly started, the
contracted column below issued
with beautiful smoothness and symmetry."

After communicating the preceding extract from a letter
which he had received from Mr Froude, Sir W. Thomson said
that on receiving the letter he had been greatly struck with this
passage, as containing the first rigorous investigation of the vena
contracta, otherwise than by experiment, which had hitherto been
made; and that he had therefore asked for and obtained permission
from Mr Froude to communicate it to the Philosophical Society.
He referred to a letter from Sir Isaac Newton to Cotes, in which
the area of the contracted vein in the case of water issuing from
a circular aperture in a thin plate was explained by the convergence
of the stream lines of the liquid flowing towards the aperture ;
and an experiment was described in which he (Newton) had
actually measured the diameter of the contracted vein, and found
it to be |^ of the diameter of the orifice. This makes the area
of the contracted vein (f J)2, or '7058 of the area of the orifice.
Froude's dynamical reasoning, which shows the area of the con-
tracted vein to be exactly half the area of the orifice in the case
of the introverted tube, shows that it must be more than half the

90

PAPERS RELATING TO MOTION OF FLUIDS

[15

area of the orifice in the case in which water flows from an
aperture in a thin plate, which is remarkably in agreement with
Newton's experiment.

Sir W. Thomson promised to append to the present com-
munication an extract from Newton's letter, which is contained
in a volume of Correspondence of Sir Isaac Newton and Professor
Cotes, including Letters from other Eminent Men, published in
1850 by Mr J. Edleston, Fellow of Trinity College, Cambridge,
from originals in the Library of Trinity College. The following,
accordingly, is the extract from Newton's letter, with a foot-note
by Mr Edleston, which is interesting as showing the origin \>f the
term "vena contracta": —

NEWTON TO COTES.

"SIR,

"Sx MARTIN'S STREET, BY LEICESTER FIELDS,
March 24M, 171?.

* * * "That you may have the clearer Idea of the
experiments in the beginning of the inclosed paper, let ABCD

represent a vessel full of water, perforated in the side with a
small hole EF made in a very thin plate of sheet tin. And
conceive that the water converges towards the hole from all parts
of the vessel and passes through the hole with a converging
motion, and thereby grows into a smaller stream after it is past
the hole than it was in the hole. In my trial the hole EF was
| of an inch in diameter, and about half an inch from the hole

1876] ON THE "VENA CONTRACTA " 91

the diameter of the stream RS* was but fj °f an inch. And
therefore the streame had the same velocity as if it had flowed
directly out of a hole but f ^ of an inch wide. And so in Marriott's
experim* the stream had the same velocity as if it had flowed
directly out of a hole but -ffa of an inch wide. In computing the
velocity of the water wch flows out, we are not to take the
diameter of the hole for the diameter of the streame, but to
measure the diameter of the streame after it is come out of the
hole and has formed itself into an eaven and uniform streame.
And the velocity thus found will be what a body would get in
falling from ye top of the water; as is manifest also by the
distance, CG, to which the stream will shoot itself, and also by
the streams ascending as high as the top of ye water stagnating
in the vessel, if the motion be turned upwards.

" I am

" Your most humble & most obliged servant,

"IS. NEWTON.

"For the Eevi Mr Eoger Cotes, Professor of Astronomy,
at his Chambers in Trinity College, in the University
of Cambridge."

(The following communication from Professor James Thomson,
LL.D., C.E., relating to Sir William Thomson's Paper, and to the
Discussion upon it, was submitted to the Committee on Papers on
31st March, 1876, and is inserted by authority of the Committee.)

PROPOSITION.

It is proposed to prove that in a jet of water issuing from a
circular orifice either in a thin plate (as in fig. 1), or at the
extremity of a round nozzle protruding (as in fig. 2), or re-entrant
(as in fig. 3), but convergent in every case towards the orifice,
the cross-sectional area of the "vena contracta," where the water
begins to have sensibly parallel stream lines, is more than half

* " RS is the diameter of the ' sectio venae contract^' (a term first used by
Jurin, Phil. Trans. Sept. — Oct. 1722, p. 185 ; and afterwards by Dan. Bernouilli,
Hydrodynam. p. 65. Jurin also uses ' vena contracta ' to denote the same thing,
and the expression is still retained in works on Hydrostatics, though differently
defined by different writers, most of them describing it as that part of the issuing
fluid between the orifice and the section whose diameter is RS)."

92

PAPERS RELATING TO MOTION OF FLUIDS

[15

the area of the orifice ; and that this condition only ceases for a
re-entrant nozzle when that (as in fig. 4) ceases to be convergent,
and becomes the re-entrant tube treated of in Mr Froude's

Fig. i.

Fig. 2.

Fig. 3.

Fig. 4.

hydraulic theorem, which has been laid before the Society in
Sir William Thomson's communication.

This proposition is to be understood as being stated only for
orifices very small in comparison to their depth below the free
surface level of the statical water ; and it may be noticed that it

1876] ON THE "VENA CONTRACTA " 93

is only this case that has usually been contemplated in statements
as to the form of the contracting vein, from the time of Sir Isaac
Newton's investigations on this subject down to present times.
The demonstration is also dependent on the supposition that in
cases of this kind the influence of fluid friction or viscosity may
without important error be neglected. It is also to be observed
that the scope of the proposition is limited to jets from circular
orifices; because, for jets from orifices of other forms than the
circular, there is no place that can properly be called the contracted
vein with flow along stream lines sensibly parallel.

Let a denote the area of cross-section of the contracted vein
where the stream lines are parallel.

Let h be the depth from the still-water surface-level in the
cistern to the centre of the orifice.

Let v be the velocity at the contracted vein, a velocity which
we know in this case must be = \f2gh.

Let p denote the density of the water, expressed as the mass
per unit of volume.

Thus we have

Volume per second = a v
Mass per second = pa

and therefore,

Momentum per second in direction of the flow = pa - 2gh.

But the unbalanced force given by the vessel to the water in a
horizontal direction in the case shown in fig. 1, when the orifice
is in a vertical plate, or when the flow at the contracted vein is
horizontal, must be equal numerically to the momentum produced
per second*. This is founded on a well-known dynamic principle,
and is easily proved, and need not be demonstrated in detail here.
Now the reaction force received by the vessel from the water is a
force the same in amount but opposite in direction. Let this be
denoted in amount by R. Thus we have

R = pa • 2gh ;

* It is to be understood that the forces referred to in the present paper are
expressed numerically in kinetic units of force, according to the method of Gauss;
or that the unit of force is the force which, acting on a unit of mass for a unit of
time, will impart to it a unit of velocity.

94

PAPERS RELATING TO MOTION OF FLUIDS

[15

and now we see that this, being double of gpah, is double the
gravity of a column having a, the cross-section of the contracted
vein, for cross-section, and h for height.

Suppose now the orifice to be at first stopped with a closely
fitting but frictionless cylindrical plug, like a piston, as in fig. 5,
and that the plug is afterwards removed to allow the water to
flow. While the close fitting but frictionless piston or plug is in
the orifice, and is held there against the water-pressure by an

Force =R! ^

Fig. 5.

externally applied force, the water's reaction against the cistern,
which may be called Rlt will be equal to the water-pressure on
the plug — that is —gpAh, where A is put to denote the area of
the orifice. On removal of the piston the water-pressure on the
remote face of the cistern, where the water has no important
velocity, remains unaltered, but some pressure round the margin
of the orifice, represented by the arrows at C and Z), is removed.
Let this abatement of pressure or of force applied to the vessel

1876]

ON THE "VENA CONTRACTA "

95

in a direction parallel to the motion of the water in the con-
tracted vein be denoted by P, and let R be put to denote the
total reaction force on the vessel when the jet is flowing; then
we have

or,

But we saw before that

R = 2gpah.
gpAh + P = 2gpah,

Hence,
or,

which is what was to be proved, as it shows that a is more
than A.

Fig. 6.

The same mode of proof applies obviously to show that the like
result holds good for all cases of the contracted vein issuing from
a circular orifice at the extremity of a round nozzle convergent
towards the orifice, and that the condition only ceases to hold
when the case of the re-entrant tube is reached, which has been
investigated by Froude, and treated of in the preceding paper of

96 PAPERS RELATING TO MOTION OF FLUIDS [16

Sir William Thomson. Also, further, it will become obvious in
like manner that when that case of the re-entrant cylindric tube
is surpassed, as in fig. 6, so that the re-entrant nozzle is divergent
towards the orifice, but still such as to permit the water to spout
off from the edge of the orifice and to contract, without having
further contact with the nozzle, the cross-sectional area of the jet
at the place called the "vena contracta" is less than half the area
of the orifice.

16. ON THE ORIGIN OF WINDINGS OF RIVERS IN ALLUVIAL
PLAINS, WITH REMARKS ON THE FLOW OF WATER ROUND
BENDS IN PIPES.

[From the Proceedings of the Royal Society, 4th May, 1876.]

IN respect to the origin of the windings of rivers flowing
through alluvial plains, people have usually taken the rough
notion that when there is a bend in any way commenced, the
water just rushes out against the outer bank of the river at the
bend, and so washes that bank away, and allows deposition to
occur on the inner bank, and thus makes the sinuosity increase.

Fig. 1.

But in this they overlook the hydraulic principle, not generally
known, that a stream flowing along a straight channel and thence
into a curve must flow with a diminished velocity along the outer
bank, and an increased velocity along the inner bank, if we regard
the flow as that of a perfect fluid. In view of this principle, the
question arose to me some years ago: — Why does not the inner
bank wear away more than the outer one? We know by general
experience and observation that in fact the outer one does wear

1876] ORIGIN OF WINDINGS OF KIVERS IN ALLUVIAL PLAINS 97

away, and that deposits are often made along the inner one. How
does this arise ?

The explanation occurred to me in the year 1872, mainly as
follows : — For any lines of particles taken across the stream at
different places, as A^, A2B2, etc. in fig. 2, and which may be
designated in general as AB, if the line be level, the water-
pressure must be increasing from A to B, on account of the
centrifugal force of the particles composing that line or bar of
water ; or, what comes to the same thing, the water-surface of the
river will have a transverse inclination rising from A to B. The
water in any stream-line CDE* at or near the surface, or in any
case not close to the bottom, and flowing nearly along the inner
bank, will not accelerate itself in entering on the bend, except in
consequence of its having a fall of free level in passing along
that stream-line f.

Fig. 2.

But the layer of water along the bottom, being by friction
much retarded, has much less centrifugal force in any bar of its
particles extending across the river ; and consequently it will flow
sidewise along the bottom towards the inner bank, and will, part

* This, although here conveniently spoken of as a stream-line, is not to be
supposed as having really a steady flow. It may be conceived of as an average
stream-line in a place where the flow is disturbed with eddies or by the surround-
ing water commingling with it.

f It must be here explained that by the free level for any particle is to be
understood the level of the atmospheric end of a column, or of any bar, straight
or curved, of particles of statical water, having one end situated at the level of the
particle, and having at that end the same pressure as the particle has, and having
the other end consisting of a level surface of water freely exposed to the atmosphere,
or else having otherwise atmospheric pressure there; or, briefly, we may say that
the free, level for any particle of water is the level of the atmospheric end of its
pressure-column, or of an equivalent ideal pressure-column.

T. 7

98

PAPERS RELATING TO MOTION OF FLUIDS

[16

of it at least, rise up between the stream-line and the inner bank,
and will protect the bank from the rapid scour of that stream-line
and of other adjacent parts of the rapidly flowing current ; and as
the sand and mud in motion at the bottom are carried in that
bottom layer, they will be in some degree brought in to that
inner bank, and may have a tendency to be deposited there.

On the other hand, along the outer bank there will be a general
tendency to descent of surface-water which will have a high
velocity, not having been much impeded by friction ; and this will
wear away the bank and carry the worn substance in a great
degree down to the bottom, where, as explained before, there will
be a general prevailing tendency towards the inner bank.

Now, further, it seems that even from the very beginning
of the curve forward there will thus be a considerable protection
to the inner bank. Because a surface stream-line CD, or one not
close to the bottom, flowing along the bank which in the bend
becomes the inner bank, will tend to depart from the inner bank

Fig. 3.

at D, the commencement of the bend, and to go forward along
DE, or by some such course, leaving the space G between it and
the bank to be supplied by slower-moving water which has been
moving along the bottom of the river perhaps by some such
oblique path as the dotted line FG.

It is further to be observed that ordinarily or very frequently
there will be detritus travelling down stream along the bottom
and seeking for resting-places, because the cases here specially
under consideration are only such as occur in alluvial plains ; and
in regions of that kind there is ordinarily*, on the average, more

* That is to say, except when by geological changes the causes which have been
producing the alluvial plain have become extinct, and erosion by the river has
come to predominate over deposition.

1876] ORIGIN OF WINDINGS OF RIVERS IN ALLUVIAL PLAINS 99

deposition than erosion. This consideration explains that we need
not have to seek for the material for deposition on the inner bank
in the material worn away from the outer bank of the same bend
of the river. The material worn from the outer bank may have
to travel a long distance down stream before finding an inner
bank of a bend on which to deposit itself. And now it seems very
clear that in the gravel, sand, and mud carried down stream along
the bottom of the river to the place where the bend commences,
there is an ample supply of detritus for deposition on the inner
bank of the river even at the earliest points in the curve which
will offer any resting-place. It is especially worthy of notice that
the oblique flow along the bottom towards the inner bank begins
even up stream from the bend, as already explained, and as shown
by the dotted line FG in fig. 3. The transverse movement
comprised in this oblique flow is instigated by the abatement of
pressure, or lowering of free level, in the water along the inner
bank produced by centrifugal force in the way already explained.
It may now be remarked that the considerations which have in
the present paper been adduced in respect to the mode of flow of
water round a bend of a river, by bringing under notice, conjointly,
the lowering of free level of the water at and near the inner bank,
and the raising of free level of the water at and near the outer
bank relatively to the free level of the water at middle of the
stream, and the effect of retardation of velocity in the layer
flowing along the bed of the channel in diminishing the centrifugal
force in the layer retarded, and so causing that retarded water,
and also frictionally retarded water, even in a straight channel of
approach to the bend, to flow obliquely towards the inner bank,
tend very materially to elucidate the subject of the mode of flow
of water round bends in pipes, and the manner in which bonds
cause augmentation of frictional resistance in pipes, a subject
in regard to which I believe no good exposition has hitherto been
published in any printed books or papers ; but about which various
views, mostly crude and misleading, have been published from
time to time, and are now often repeated, but which, almost
entirely, ought to be at once rejected.

7—2

100 PAPERS RELATING TO MOTION OF FLUIDS [17

ORIGIN OF THE WINDINGS OF RIVERS IN ALLUVIAL PLAINS.

[From the Glasgow Herald of Sept. 8, 1876. Report of the British
Association Meeting at Glasgow.]

Professor James Thomson submitted an experimental illus-
tration of the origin of windings of rivers in alluvial plains. The
Professor referred to a communication which he made to the Royal
Society in the month of May last, and which was subsequently
published in Nature*. In that communication he had given a
new theory of the motion of water in round bends in rivers and
in pipes, and had explained the reason why in alluvial plains the
bends of rivers go on increasing by the wearing away of the outer
bank and the deposition of mud, sand, and gravel on the inner
bank. The theoretical view which he had then formed he now for
the first time had verified by practical experiment, and this
experiment he showed in the meeting. The chief point of the
new view now experimentally proved was that the water in
turning the bend has centrifugal force, but a thin bed of the water
at the bottom is retarded by friction with the bottom, and so has
less centrifugal force than the great body of the water flowing
over it. Consequently the bottom layer flows onward obliquely
across the channel towards the inner bank, and rises up in its
retarded condition between the inner bank and the rapidly flowing
water, and protects the inner bank from the scour, and brings
with it sand and other detritus from the bottom, which it deposits
along the inner bank. A working apparatus, he further stated,
had been placed in the Kelvingrove Museum.

17. EXPERIMENTAL DEMONSTRATION IN RESPECT TO THE ORIGIN
OF WINDINGS OF RIVERS IN ALLUVIAL PLAINS, AND TO THE
MODE OF FLOW OF WATER ROUND BENDS OF PIPES.

[From the Proceedings of the Royal Society, No. 182, 1877.]

In a paper which I had the honour of submitting to the
Royal Society rather more than a year ago, and which is printed
in the Proceedings for May 4, 1876, I proposed, on hydrokinetic
principles, a theoretical view of the mode of flow of water round

* [No. 16 supra ; reprinted in Nature, Vol. xiv. p. 122. June 1, 1876.]

1877] ORIGIN OF WINDINGS OF RIVERS IN A^LUVtAL: I^LAINlS

bends of rivers and of pipes, and offered under that view
explanations of the origin of the windings of rivers flowing
through alluvial plains. Wishing to bring under the test of
experiment the views then put forward, and to render very clearly
perceptible the phenomena anticipated, I constructed, in the
summer of 1876, a small artificial river, about eight inches wide
and an inch or two deep, having a bend turning about a half-round,
or 180°, so that the course of the river might be likened to the
capital letter U. The water flowing in this river showed very
completely, and very remarkably, the phenomena which had been
anticipated, and which are to be found described in the paper
referred to. The courses of the water's flow at the various parts
of the river, along the bed, and at the upper surface, and at places
anywhere within the body of the current, were made to show
themselves in several ways. One way was by means of threads of
suitable length (about an inch or two long), some of which were
anchored at bottom, while others were attached at various depths
in the river to pins or slender wires standing upright like thin
posts in the river. These threads, by the lines of direction which
they assumed, showed very well the directions of the flow at
bottom and at various depths. Another way, and one which
proved very satisfactory for showing the bottom currents, was by
dropping into the river granules of various kinds, such as sand,
and peas selected of good round form, and other small round seeds,
such as clover-seed and poppy-seed. Granules such as these
showed very clearly numerous phenomena, not only of the flow
of the water, but also of the transmission of material like detritus
forward along the bottom in straight parts, and very obliquely
across the bottom in the bend; and gave imitations on a small
scale, easy for observation, of the processes of accumulation of
detritus along the inner banks of the bends of rivers, and pre-
sented also interesting suggestions and considerations as to some
of the details or secondary actions involved in the processes*.

* The experiments here described were shown in the Mathematical and Physical
Section of the British Association at the meeting held at Glasgow, in September
1876, and further in the temporary collection prepared in the Kelvingrove Museum
at Glasgow, for that meeting of the Association. As they were arranged expressly
for testing and illustrating the theoretical views contained in a paper previously
submitted to the Royal Society, the present brief account of them is offered here to
the Society as a sequel to that previous paper.

102 PAPERS RELATING TO MOTION OF FLUIDS [18

18. ON THE FLOW OF WATER ROUND RIVER BENDS.

[From the Proceedings of the Institution of Mechanical Engineers. Read at a
meeting in Glasgow, 6th August, 1879.]

Professor James Thomson, F.R.S., gave a short description of
an apparatus, figs. 1 and 2 [p. 103], illustrative of the mode of
the flow of water round bends of rivers, and also round bends of
pipes. On this subject he had long felt dissatisfied with all such
views as had been put forward; and had considered that the
various formulae which had been published in regard to the resist-
ance offered by bends in pipes to the flow of water, and which had
long been in use, more or less, among hydraulic engineers, were
certainly not founded on any reasonable theory whatever of the
behaviour of the water. Lately a new view had occurred to him,
which he had brought before the Royal Society; and he had
afterwards constructed an experimental apparatus which gave
confirmation to the theory, by exhibiting very distinctly the
phenomena which the theory had led him to anticipate. This
apparatus, it was thought, would be of interest to members of the
Institution of Mechanical Engineers ; and arrangements were
made for showing it in action in an adjoining room.

In the windings of rivers in alluvial plains, such as were
manifested very strikingly in the Mississippi and Ohio rivers,
and indeed all over the world in rivers whether large or small,
there were very interesting phenomena and considerations involved,
both as to hydraulic questions, and as to questions of physical
geography : both in reference to the behaviour of the water, and
in reference to the modes of growth or modes of change of the
river bends. It was well known that, in rivers flowing in alluvial
plains, windings, already existing, tended to go on increasing by
the scouring away of material from the outer bank, and the
deposition of detritus along the inner bank. The sinuosities often
went on increasing till a loop was formed, with only a narrow
isthmus of land left between two encroaching banks of the river ;
and the process continued till a " cut off" occurred, a short passage
for the water being opened through the isthmus, and the loop
being left separated from the river course and remaining as a

1879] ON THE FLOW OF WATER ROUND RIVER BENDS 103

Outer JBank

Section, a,t M "N.

Fig. 2.

104 PAPERS RELATING TO MOTION OF FLUIDS [18

horse-shoe shaped lagoon or swamp, often, in the case of large
rivers, stretching as much as five or ten miles away from the new
course of the river channel. The usual supposition had been that
the water, tending always to go directly forward in the straight
line of its existing course, simply rushed outwards against the
outer bank and wore it away, and at the same time caused deposits
at the inner bank; and that thus sinuosities when once begun
tended to increase. That view was not wrong, but it was very far
from the whole truth. There was an important principle in
hydraulics, which was not very commonly known, and the bearing
of which on the present subject did not appear to ha?e been
noticed in any of the theories which had been advanced previously
to his own. This was the principle that water flowing round a
bend would necessarily, according to true dynamical theory and
according to actually observed facts, get to run more quickly in
feet per second near the inner bank than near the outer bank.
An illustration of that might be seen in an ordinary wash-hand
basin, which, when the water was whirled round a little and the
plug withdrawn, presented approximately the " whirlpool of free
mobility*." As the water flowed in towards the centre, the character
of the whirlpool approached very closely to that of a true whirlpool
of free mobility, in which the linear velocity was throughout
inversely proportional to the distance from the centre : so that not
only the angular velocity, but the linear velocity in feet per second
was increased as the water flowed towards the centre. The water
flowing inwards in a whirlpool might be regarded virtually as if
flowing downhill, or more properly it was to be regarded as actually
flowing from a region of higher to a region of lower free level "f;
and it must thus acquire the accession of velocity due by gravity
to its descent, in the case of a particle flowing down the open
surface, or to the fall of free level, in the case of a particle flowing
within the body of the whirlpool.

It was very much in the same way, and for like reasons, that
the water in a river bend flowed more quickly along courses adjacent
to the inner bank of a river bend than along courses adjacent to
the outer. Hence the question had occurred to him : — why then
did not the inner bank wear away more ? As a matter of fact we

* [Supra, p. 1.]

f [A footnote repeating the definition of free level given in the note on p. 97
supra is omitted.]

1879] ON THE FLOW OF WATER ROUND RIVER BENDS 105

knew that it did not ; but why was this so, if the water scoured
more quickly along the inner bank than along the outer ? For a
long time he could not explain this ; but afterwards he had found
the true explanation. The water of a river, in flowing round a
bend, pressed outwards in virtue of centrifugal force, and so there
was a transverse slope of the water surface rising from the inner
bank towards the outer, as shown in the cross section, fig. 2
[p. 103]. Thus at any one level in the stream there was for this
reason a greater pressure near the outer bank than near the inner.
The case might be better stated thus. The free level for any
particle of the water near the outer bank was higher than the
free level for any particle near the inner bank at the same level
and in the same cross section ; and the water tended to flow from
the place of higher free level to the place of lower free level ; but
the centrifugal action kept the water outwards against that inward
tendency.

Further the most special point of the explanation was the
following. At the resisting bottom there was a thin lamina of
water at all times prevented by fluid friction, or viscosity, from
having sp high a velocity as the general average velocity of the
body of the stream above it ; and consequently it had not enough
centrifugal force to keep it out against the inward tendency given
by the higher free level at the outside than at the inside. Thus
the water at the bottom must have a prevailing tendency from the
outer bank towards the inner, and must tend to carry inwards
with it gravel, sand, mud, and other detritus, and leave them
deposited at the inner bank. Conjointly with this inward flow at
the bottom, there must be in the middle and upper body of the
stream a prevailing flow towards the outer bank ; but the outward
flow would be more gentle than the inward, being participated in
by a much larger body of water.

That theory he had submitted to the Royal Society in a paper*
read 4th May 1876, and printed in the Proceedings of the Society,
1876, p. 5. Afterwards he had proceeded to test it experimentally,
and the experiments turned out completely to verify the theory f.
An artificial channel, on a small scale, including a bend, was formed
in imitation of a river, and upright pins were stuck into the bottom,
like posts in a channel ; to these pins little pieces of thread were
attached, some at the bottom, some at the water surface, and some

* [Supra, p. 96.] t [Supra, p. 100.]

106 PAPERS RELATING TO MOTION OF FLUIDS [19

at intermediate levels. These, like flags flying, showed the different
directions of the currents at different depths. The courses of the
bottom currents, and their action in carrying detritus across the
channel in the bend towards the inner bank, so as to form
accumulations at or adjacent to the inner bank, were brought
into notice by throwing in sand and small seeds in imitation
of detritus.

In the apparatus, as fitted up in an adjoining room for this
meeting of the Institution of Mechanical Engineers, the phenomena
would be shown by the use of seeds serving as detritus, and small
objects floating on the surface; and also in a new way* by little
specks of aniline dye introduced so as to adhere to the bed of the
channel at various places on the bottom and banks under water.
From each speck of the adhering dye, the flowing water carried
forward colouring matter, which showed that the course of the thin
film of the stream, close to the bed, was along lines such as CC in
the plan, fig. 1, the stream there flowing strongly towards the
inner bank; while a floating object placed on the water surface
would move along a line such as AB, in fig. 1, going towards the
outer bank. The whole of the upper part of the river flowed out-
wards slowly, while the stream along the bottom flowed inwards
very quickly. There was a little eddy at D, fig. 2, whose existence
was manifested very clearly by the aniline dye. The theoretical
considerations connected with this eddy were very interesting;
but, for brevity, he would not enter upon its discussion on that
occasion.

19. ON THE FLOW OF WATER IN UNIFORM REGIME IN
RIVERS AND OTHER OPEN CHANNELS.

[From the Proceedings of the Royal Society, No. 191, 1878.]

In respect to the mode of flow of water in rivers, a supposition
which has been very perplexing in attempts to form a rational
theory for its explanation, has during many years past, during at
least a great part of the present century, been put forward as
a result from experimental observations on the flow of water in

* [Suggested by Mr, now Professor, Archibald Barr.]

1878] ON THE FLOW OF WATER IN UNIFORM REGIME 107

various rivers, and in artificially constructed channels. It was,
I presume, put forward in the earlier times only as a vague and
doubtful supposition ; but, in later times it has, in virtue of more
numerous and more elaborately conducted experimental observa-
tions, advanced to the rank of a confirmed supposition, or even of
an experimentally established fact. This experimentally derived
and gradually growing supposition was perplexing, because it was
in conflict with a very generally adopted theory of the flow of
water in rivers which appeared to be well founded and well
reasoned out.

That commonly received theory, which for brevity we may call
the laminar theory, was one in which the frictional resistance
applied by the bottom or bed of the river against the forward
motion of the water was recognized as the main or the only
important drag hindering the water, in its downhill course under
the influence of gravity, from advancing with a continually in-
creasing velocity ; and in which it was assumed that if the entire
current is imagined as divided into numerous layers approximately
horizontal across the stream, or else trough-shaped so as to have
a general conformity with the bed of the river, each of these
layers should be imagined as flowing forward quicker than the one
next below it, with such a differential motion as would generate
through fluid friction or viscosity, or perhaps jointly with that,
also through some slight commingling of the waters of contiguous
layers, the tangential drag which would just suffice to prevent
further acceleration of any layer relatively to the one next below
it. Under this prevailing view it came to be supposed that for
points at various depths along any vertical line imagined as
extending from the surface of a river to the bottom, the velocity
of the water passing that line would diminish for every portion of
the descent from the surface to the bottom.

The experimentally derived and perplexing supposition for
which no tenable theory appears to have been proposed, though
the want of such a theory has been extensively felt as leaving the
science of the flow of water in rivers in a state of general
bewilderment, is, that inconsistently with the imagination of the
water's motion conceived under the laminar theory, the forward
velocity of the water in rivers is, in actual fact, sometimes or
usually not greatest at the surface with gradual abatement from
the surface to the bottom; but that when the different forward

108 PAPERS RELATING TO MOTION OF FLUIDS [19

velocities are compared which are met with at successive points
along a vertical line traversing the water from the surface to the
bottom, it may often be found that the velocity increases with
descent from the surface downwards through some part of the
whole depth, until a place of maximum velocity is reached, beyond
which the velocity diminishes with further descent towards the
resisting bottom.

That the superficial stratum of water flowing downhill under
the influence of the earth's attraction should not have its forward
velocity continually accelerated until, by its moving quicker than
the bed of water on which it lies, a frictional drag wo\ild be
communicated to it from below, by that supporting bed of water,
sufficient to hold it back against further acceleration, has appeared
very paradoxical. In various cases, during a long period of time,
the alleged result appeared so incredible that the experimental
evidence was doubted, or was dismissed as untrustworthy. In
some cases the phenomenon was admitted as a fact, but was
attributed to a frictional drag or resistance applied to the surface
of the water by the superincumbent air, even in case of the air
being at rest with the water flowing below, or more strongly
so when the wind might be blowing contrary to the motion of
the river.

Omitting to touch on the experimental results, and the
opinions of various investigators in the older times, as I have not
had sufficient opportunity to scrutinise them in detail, I have to
refer to the investigations conducted at about the year 1850 by
Ellet on the Mississippi and Ohio Rivers*. He was led to the
conclusion •(• from his own experiments on the Mississippi, that the
mean velocity of that river (or at least the mean velocity of the
great body of its current, as the part near the bottom or bed
of the river had not been definitely included in his researches)
instead of being less, is in fact greater than the mean surface
velocity. He attributed this phenomenon, which he regarded as
indubitably proved, and which if true must certainly be very
remarkable, to a frictional drag or resistance, against the forward
motion, applied to the surface of the water by the atmosphere in

* Ellet on the Mississippi and Ohio Rivers. Philadelphia : 1853. This is a
republished edition of a Report to the American War Department by Ellet on his
investigations, which were made under authority of an Act of Congress.

t Pages 37 and 38 of the book referred to in the preceding note.

1878] ON THE FLOW OF WATER IN UNIFORM REGIME 109

contact with the surface. Like suppositions had previously been
made by some observers and theoretical investigators in Europe,
as may be gathered from D'Aubuisson, Traite d'Hydraulique, 2nd
edition, 1840, p. 176, and from other sources of information.

Other experimental researches on the flow of the Mississippi
River, much more elaborate than those of Ellet, were made in the
period between 1850 and 1861 by Captain Humphreys and
Lieutenant Abbot, with others acting under authority from the
American Government, and an account of them was published as
a Report by Humphreys and Abbot in 1861*. These experiments
and the investigations exhibited in the report, where the observed
results are combined in various ways so as to bring out average
results and more or less probable conclusions for various circum-
stances, lead very clearly and very convincingly to the conclusion
that ordinarily the maximum velocity is not at the surface but at
some depth below it, usually much nearer to the surface than to
the bottom, and often at some such depth from the surface as
J or ^ of the whole depth of the water. These investigators
(Humphreys and Abbot) show further (at pages 285, 288, and
289 of their Report) that this phenomenon is not wholly nor even
mainly due to any frictional resistance applied by the super-
incumbent atmosphere to the forward flow of the surface of the
water ; because they found that even when the wind is blowing in
the direction of the river current, and advancing at the same
velocity as that current, so that the air lies on the surface of the
water without relative motion, the phenomenon manifests itself
almost in as great a degree as when the air is lying at rest
relatively to the land ; and found yet further that the phenomenon
still manifests itself even when the wind is blowing in the
direction of the flow of the river much faster than the current,
so that it blows the water surface forward instead of applying
a resisting drag or backward force to the surface.

At about the middle of the present century very important
experiments on flowing water were made in France by Boileau,
and by Darcy and Bazin ; and elaborate accounts of these researches
were published f.

* Report on the Physics and Hydraulics of the Mississippi River. By Captain
A. A. Humphreys and Lieutenant H. L. Abbot. Philadelphia: 1861.

t Boileau : Traite de la mesure des eaux courantes. Paris : 1854. Darcy : Recher-
ches experimentales relatives au mouvement de Veau dans les tuyaux. Paris : 1857.

110 PAPERS RELATING TO MOTION OF FLUIDS [19

The experiments comprised among the researches of Boileau
and of Darcy and Bazin, to which I have to refer as bearing on
the special subject of the present paper, relate to the flow of
water in long channels and conduits constructed artificially, some
in wood and some in masonry and other materials. The channels
or conduits in different cases were of widths comprised between
half a metre and two metres. In some of the more important
experiments the channels were constructed in wood, and were
open above, and had a flat bottom and vertical sides, so that the
current was rectangular in cross section. Channels of various
other forms were also used, and the mode of flow of the water in
them was scrutinized. The results arrived at by these experimenters
tend very much towards establishing the supposition which forms
the subject of the present paper — the supposition, namely, of the
prevalence or frequent occurrence of a distribution of velocities
having the maximum velocity not at the surface but at some
moderate depth below. Boileau, by his experiments, was led to
announce as one of his conclusions (page 308), that in the medial
longitudinal vertical section of a rectangular canal with uniform
regime, the maximum of velocity is situated not at the surface,
but at a depth which is a fraction more or less considerable of the
total depth of the current. He also announced, as a conclusion,
that the decrease of velocity, from the place of maximum velocity
up to the surface, must be attributed to some new cause different
from that which produces the diminution of velocity from the
place of maximum down to the bottom. This new cause, he says,
cannot be solely the resistance of the bed of air in contact with
the liquid surface acting like the face of a pipe or conduit ; and
he assigns, in proof of this, the reason that the mobility of this
bed of air does not permit of our attributing to it a retarding
influence so great as that which is implied in the rapid abatement
of velocities in approach towards the surface in the upper part of
the current. He recounts his own special experiments, made in
1845, on the influence of wind on the velocities in currents, —
a subject which he says had up to that time been very little

Darcy et Bazin : Recherches Hydranliques. Paris : 1865. This last book con-
stitutes a memoir by Bazin on researches commenced by Darcy, and continued
for some time by him with the aid of Bazin ; and, after the death of Darcy in 1858,
continued by Bazin, and by him completed and worked out in the discussion of
their results.

1878] ON THE FLOW OF WATER IN UNIFORM REGIME 111

investigated by hydrauliciaiis. He deduces from his experiments
conclusions (page 313) to the effect that in spite of varied
disturbances produced by wind blowing over the water with
varied intensity, yet there is manifested a very sensible tendency
to a decrease of velocities of the water for approach towards the
liquid surface ; and that the maximum velocity is yet below the
surface, even when the wind blows forward with the current, and
has a velocity greater than that of the current. Judging, then,
that resistance of the air cannot be the cause of the phenomenon,
he says that it is then principally in the mutual actions which
bind among one another the liquid particles, and in the oblique
and rotatory movements which result, under the influence of these
forces, from the difference of velocities of neighbouring particles,
that it is necessary to seek for the explanation of the phenomena
of the decrease of velocities in the approach towards the surface
of currents. He goes on to say that we have to conceive, in fine,
that these oblique movements, producing transverse living forces
(forces vives), diminish, according to certain general laws, the
living forces of forward motion which the hydrometric instruments
are adapted to indicate.

I have cited this passage from Boileau very fully, because it
seems to me to contain the nearest approach towards an explanation
of the phenomenon in question of any that have been attempted,
so far as any such attempts have come under my notice. It
involves, I think, at least a glimmering towards a true explanation ;
but I regard it as being in great part erroneous, and importantly
so in principle, and as being besides altogether incomplete. I do
not think it has been offered by the very able investigator himself,
who has proposed it, as being at all sufficient ; but I think it has
been offered only as tending to throw some light over the region
for further search, and some indication towards courses in which
speculation and research might well advance.

Bazin's experiments, of the general character already mentioned,
were very extensive in their scope, and were carried out in great
detail, and with some remarkable refinements of method. The
velocities were measured mainly or wholly by a modification
devised by Darcy of the well-known instrument called Pitot's
tube. Bazin, in the case of canals not very wide relatively to the
depth of the current, found very clearly and decisively the pheno-
menon in question of the maximum velocity being below the

112 PAPERS RELATING TO MOTION OF FLUIDS [19

surface. But, in the case of rectangular channels of more con-
siderable width, channels having the width of the current so much
as four or five times the depth or more, Bazin by his scrutiny and
consideration of his experimental results, was led to conclude
that the diminution of velocity for approach towards the surface
in the upper part of the current is to be found only in the side
parts of the current — the parts flowing along the two side walls.
He judged that throughout the whole of the current, except two
side parts, each having some moderate width, which might be
equal to about twice the depth of the current, the maximum of
the velocities for all points, situated in a vertical line, i$ to be
found at the surface ; and that the rate of diminution of velocity
for descent from the surface would begin as nothing at the surface,
and would go on increasing with descent to the bottom. His
experiments, according to his own careful analysis and combination
of them, appeared to be in agreement with this assumption, or to
bring this supposition out as a result.

I do not, however, regard this conclusion as being trustworthy.
His experiments for the case of great width relatively to depth
had not, in any instance, a depth of water exceeding '38 of a metre,
or 1J foot, and thus the depths were so small absolutely as not to
admit of a fine enough discrimination of minute changes of
velocity for minute changes of depth of the point where the
velocity was observed, nor of measuring velocities close enough to
the surface. So far as experimental researches go, some doubt
I presume must still remain over this part of the subject. Indeed,
the Indian experiments, next to be mentioned, show results in
disagreement with this conclusion offered by Darcy.

Quite recently, in 1874-75, experiments were conducted in
India on the Ganges Canal, close to Roorkee, by Captain Allan
Cunningham, R.E.* These experiments bring out among their
results, very remarkably, the frequently alleged phenomenon of
the maximum velocity of the water being not at the surface, but
at some moderate depth below. And further, it is deserving of
special notice that those of his experiments, which have chiefly to
be referred to as throwing light on this subject, were made in an
aqueduct about 85 feet wide, and with an approximately level

* " Hydraulic Experiments at Roorkee, 1874-75," by Captain Allan Cunning-
ham, R.E., published in Professional Papers on Indian Engineering. Thomason,
College Press, Roorkee, 1875 : also Spon and Co., London, &c.

1878] ON THE FLOW OF WATER IN UNIFORM REGIME 113

bottom ; and that the depths of the water in different experiments
ranged from about 6 feet to about 9-|- feet, so that the width was
on different occasions from about nine times to about fourteen
times the depth, and yet the maximum of the velocities at mid-
channel (or the maximum velocity in the longitudinal medial
vertical section) came out by averages of numerous results, and,
by varied modes of experimenting, to be very decidedly below the
surface.

Experiments carried out lately on a very large scale on the
Irawaddy river by Robert Gordon, Executive Engineer, British
Burmah, Public Works Department, go to confirm the truth of
the same phenomenon. These experiments of Mr Gordon, how-
ever, although valuable in many respects, appear to be subject to
some doubt as to whether, through the mode of experimenting,
the level of supposed maximum velocity has not been brought out
too low, that is to say, too near the bottom. On this point
Mr Gordon (in his Introductory Note, § vii, p. ii of date 16th
June, 1875) intimates his intention to make further experiments
with other instruments, but still asserts his confidence in his
previous methods and results.

Until about two years ago I had not happened to become
acquainted with any of the evidence for the phenomenon in
question except the unsatisfying experimental results given by
Ellet; but about two years ago I met with accounts of some of
the more recent and more convincing experimental investigations.
It then appeared to me that if the asserted phenomenon must
really be accepted as a truth, there ought to be some mode possible
of accounting for it : and a theory occurred to me which I now
propose to submit.

The mode of thought which near the beginning of the present
paper I have described as constituting the laminar theory, I must
premise, has long appeared to me to be an erroneous and a very
misleading view. It was a very prevalent mode of thought, and
was usually too influential on people's minds even when they did
entertain decidedly, though often not clearly enough, the con-
sideration of eddies and transverse movements or commingling
currents with different velocities. The great distinction between
the mode of flow of a very viscid fluid, such as treacle or tar, and
the mode of flow of water in ordinary circumstances in pipes and
in open channels, has not been enough generally and enough

T. 8

114 PAPERS RELATING TO MOTION OF FLUIDS [19

consistently attended to. The laminar theory constitutes a very
good representation of the viscid mode of motion; but it offers
a very fallacious view of the motion in the flow of water in
ordinary cases in which the inertia of the various parts of the fluid
is not subordinated to the restraints of viscosity.

In the flow of water in an open channel in ordinary circum-
stances the earth's attraction is perpetually tending to accelerate
the forward motion of the water throughout the whole body of the
current in consequence of the surface declivity ; or we may say,
with more complete expression, in consequence of the fall of free
level* which, in virtue of the surface declivity, occurs* to all
particles in the current as they advance in their down-stream
course. The tendency to increase of velocity, if we neglect the
backward or forward force, usually very small, or it may be
nothing, applied by the air to the water surface, we may say
is counteracted solely by a backward resisting force-system applied
by the wetted face of the channel to the water momentarily in
contact with it. The wetted channel face, it must be observed, is
ordinarily more or less rough with gravel, mud, weeds, or other
asperities. It is not a true view to imagine a smooth channel face
washed by a thin lamina of water, which imagined lamina of water
receives a backward or resisting force-system applied tangentially
by the so imagined channel face, and transmits tangential backward
force to another lamina of water lying next to itself on the side
remote from the channel face. It is not the case that from any
layer of water whatever, thick or thin, spread over the channel
face, resisting forces are transmitted to the interior of the body of
the current in any great degree by mere viscid resistance to
change of form in the intervening fluid, as would be the case if it
were like treacle or tar. But, very differently, indefinite increase
of velocity of the water situated in the interior of. the current is
prevented by continual transverse flows thereto, and commingling
therewith, of portions of water already retarded through their

* The free level for any particle of water, in a mass of statical or of flowing
water, is the level of the atmospheric end of a column, or of any bar of statical
water, straight or curved, having one end situated at the level of the particle, and
having at that end the same pressure as the particle has, and having the other end
consisting of a level surface of water freely exposed to the atmosphere, or else
having otherwise atmospheric pressure there. Or, briefly, we may say that the
free level for any particle of water is the level of the atmospheric end of its pressure-
column, or of an equivalent ideal pressure-column.

1878] ON THE FLOW OF WATER IN UNIFORM REGIME 115

having been lately in close proximity to the resisting channel face ;
and, jointly with that, by the condition that portions of the fluid
which have been flowing forward temporarily in the interior of
the current, and have been gaining forward acceleration there, are
gradually expelled, or do gradually flow from that region, and
come themselves into close proximity to the resisting channel
face; and so, in their turn, do receive very directly backward
forces from the face, because in proximity to it processes of fluid
distortion subject to viscid resistance are going or with great
activity and intensity.

The transverse motions have their origin primarily in the rush
of the water along the wetted channel face. When that face
is rough or irregular with lumps and hollows or other asperities,
reasons for the origination of transverse currents may be sufficiently
obvious. But even if the channel face is extremely smooth, so as
to present no sensible asperities, still there is good reason to assert
that transverse flows will come to be instituted in consequence of
the rapid flow of the main body of the current along a lamina,
very thin it may be, of water greatly deadened as to forward
motion by viscid cohesion with the channel face, and throughout
and across which, if regarded as only very thin, in virtue of its
thinness, the backward force applied by the face can be transmitted
by mere viscosity. The thin lamina of deadened water will tend
by the scour of the quicker going water always moving subject to
variations both of velocity and of direction of motion to be driven
into irregularly distributed masses ; and these, acted on by the
quicker moving water scouring past them, will force that water
sidewise, and will be entangled with it and will pass away
with some transverse motion to commingle with other parts of the
current*.

* This principle I noticed myself in the connexion in which it is here adduced ;
and the idea has since been confirmed to me and rendered more definite through
additional considerations mentioned to me lately by my brother, Sir William
Thomson, which have originated with him in some of his theoretical investiga-
tions in quite another branch of hydraulic science, and which relate to finite slip
in a frictionless fluid. He pointed out that if, for water theoretically regarded as
frictionless, or devoid of viscosity, we imagine a long smoothly formed straight
trough or channel with a thin vertical longitudinal plane septum dividing it into
two parts each uniform in cross-section throughout its length, and if we imagine
the space on one side of the septum to be occupied by still water, and a current
to be flowing along on the other side ; and if, while this is in progress, we imagine
the vertical partition to be withdrawn so as to leave the current flowing along a

8—2

116 PAPERS RELATING TO MOTION OF FLUIDS [19

If we watch the surfaces of flowing rivers, or of tidal currents
flowing in narrows or kyles, we may often have opportunity to
observe very prevalent indications of rushes of water coming up
to the surface and spreading out there. These rushes often may
be seen to keep rising in quick succession in numerous neighbouring
parts of the water surface, and they may be seen presenting
appearances of spreading out till they meet one another and give
indication of momentary downward sinking at their places of
meeting.

From whence do these transverse currents come to the surface?
It seems to me they must have had their origin in the deadened
water scouring along the bottom, or along the wetted side-faces of
the channel, in such ways as have just now been briefly sketched
out. Thus it seems that there are tendencies bringing about the
result that the superficial stratum of the river receives perpetually
renewals of its substance by water currents arriving to it, and
spreading out there, which have very recently departed from the
bottom before coming up to enter into that superficial stratum.
But their substance, having come in great part from the bottom,
must be largely made up of the deadened or slow-going bottom-
water. It is to be understood that this deadened water, in rising
through the current towards the surface, is partly urged forward
in the down-stream direction by the surrounding quicker-going
water, but that it arrives at the surface without having attained
fully to the down-stream velocity of that intermediate stream.

It may readily be perceived that it is from the washed face of
the channel alone, or from that and the retarded layer of water in
proximity to it, that any strong transverse impulses can be applied
to any parts of the current. No rapid transverse current will
originate in the middle of the body of the river ; for there is no
cause for the origination of transverse currents there, unless
perhaps we were to regard as such any slight transverse motions
which may be produced through the gliding forward of parts of
the water there relatively to others near them going with different

plane face of still water, the motion with the finite slip thus instituted will be
essentially unstable. Keasons for this, when once it is brought under notice, are
very obvious from consideration of the centrifugal forces, or centrifugal actions,
which would be introduced on the slightest beginning being made of any pro-
tuberance or hollow in the originally plane interface between the still water and
the current. [Of. Sir William Thomson, Math, and Phys. Papers, Vol. iv.
pp. 330 et seq.]

1878] ON THE FLOW OF WATER IN UNIFORM REGIME 117

velocities, and unless we were to regard as such any transverse
disturbances that may be imparted to forward-flowing water there
by the intrusion and commingling of partially deadened water
from the channel-face.

We may now have great confidence, I think, in taking as
a well-established truth, or at least as a very probable view, the
supposition already laid down to the effect that very commonly
the superficial stratum of a river receives perpetually renewals of
its substance by water currents arriving to it and spreading out
there, which have very recently departed from the bottom or sides
of the channel before coming up to enter into that superficial
stratum; and that the substance thus perpetually renewing the
surface stratum is largely composed of deadened or slow-going
bottom-water, or of water going slower forward than the water
through which it traverses in ascending to the surface. It is
further to be noticed that the water which at any moment consti-
tutes the superficial stratum is, in its turn, very soon overflowed
by later arrivals from the bottom. So it gradually descends from
the surface into the interior of the body of the river. But during
this action it is always flowing downhill, or we may better say it
is experiencing a fall of free level, in consequence of the surface
declivity. It is thus receiving forward acceleration in the down-
hill direction, and its velocity goes on increasing until at some
depth from the surface it reaches a maximum, from whence, during
further lapse of time and further descent of this water towards
the bottom, the retarding influences imparted to it from the
bottom are predominant over the downhill accelerating influence
of gravity. These retarding influences, chiefly acting through
transverse rushes of water from the bottom commingling more
numerously and more briskly with the descending water Binder
consideration the more it gets into the neighbourhood of the
bottom, bring about the result that the water goes forward with
less and less velocity as it approaches nearer and nearer to the
bottom.

I have now to offer, by consideration of an imaginable case
different from that of an ordinary river, an illustration which will
aid in the forming of clear ideas on what I have been presenting
as a true theory of the real behaviour of the water in rivers.

Let us imagine a flowing river composed mostly of water, but
with a layer of oil floating on the top, the oil being of some such

118 PAPERS RELATING TO MOTION OF FLUIDS [19

depth as a tenth or a twentieth part of the whole depth of the
river. Let us suppose the width of the river to be so very great
relatively to the depth as that in considering the flow in a middle
portion of the river, we may regard it as experiencing no sensible
retarding influences, either through the water or the oil, from the
sides of the river ; and let the flow to be kept under consideration
be only that middle portion without the lateral portions which
would be sensibly affected by retarding influences from the sides.
Here we have a case differing from that of an ordinary river of
water in this important respect, that, while in the ordinary river
the superficial stratum of fluid is perpetually changing its substance,
and is, as I suppose, perpetually receiving new supplies of deadened
water from the bottom, in the imagined case now adduced the
substance of the superficial layer being of oil floating at top, does
not undergo any such change. The oil then, it seems very certain,
would really rush down what we may call the inclined plane
of water on which it lies, and would go on accelerating its motion
until, by advancing very much faster than the water, it would
introduce a frictional drag between itself and the water sufficient
to hinder its further acceleration*; or rather until, without

* Postscript note, 1st November, 1878. — An observed phenomenon, which, if
duly taken into consideration, must doubtless be found to be closely allied in its
nature to the supposed behaviour of the imagined layer of oil on a flowing river of
water above adduced, and which is certainly of much interest, both for its own
sake and in reference to theoretical views which have been held as to its origin and
its indications, has come under my notice since the time when the present paper
in manuscript was presented to the Royal Society. The book by Bazin, which
may be briefly named as Darcy et Bazin, Recherches Hydrauliques, Paris, 1865 (see
a previous footnote in this paper), contains prefixed to it a report, dated 1863, of
a Committee of the Academy of Sciences on the memoir of M. Bazin, " Sur le
Mouvement del'Eau dans les Canaux decou verts." In that report the committee
remark (as confirmatory of the view which they accept, to the effect that in deep
rivers, especially when not very wide relatively to their depth, the place of maxi-
mum velocity is at a considerable depth below the surface) as follows: — "II y a
longtemps que les bateliers du Rhin et nos pontonniers savent qu'un bateau charge
et ayant un fort tirant d'eau, marche, en descendant, plus vite que 1'eau qui le
soutient ou que les corps flottants a la surface." This obviously conveys the
opinion that a heavily loaded boat, sinking deep into the water, and thereby having
its deeper part immersed in water which is flowing quicker than the surface water,
is dragged forwards by that deeper and quicker moving water, and so is made to
advance quicker than the surface water does. The idea seems to be that the boat
has some average velocity less than that of the water at its bottom, and greater
than that of the surface water. The view which thus appears to be held in respect
to the observed phenomenon seems to me to be inadequate and erroneous. On the
principle put forward above in the present paper in reference to the imagined case

1878 J ON THE FLOW OF WATER IN UNIFORM REGIME 119

attaining to that stage of great relative velocity, it would at an
earlier stage ruffle up the mutual face of meeting of itself and the
water into protuberances and hollows, somewhat like waves, on
the principle referred to already in a foot-note as having been
proposed by Sir William Thomson, and would carry this action on
to the extent of causing commotion and commingling of the water
and oil. The contrast between this case and that of an ordinary
river of water is so remarkable as to aid the forming of a clear
comprehension of the very different mode of action which I have
been attributing to the water in ordinary rivers and other open
channels.

It is further worthy of notice that if, from any local cause, the
water flowing forward in some part of the width of a river has in
its motion a component downward from the surface towards the
bottom, and is free from intrusion of upward currents or rushes of
deadened water from the bottom, or of water retarded by the
influence of the river-bed, we ought to expect the forward velocity
to increase from the surface to very nearly the bottom. The
accelerative influence of gravity due to the surface inclination,
and more particularly due to the fall of free level experienced, as
an accompaniment of that inclination, by the water throughout
the body of the current in its onward flow would generate in every
portion or particle of this water increase of velocity for advance
along its course ; because, in the absence of rushes of deadened

of a river with an upper layer of oil, I would suppose that a large and heavy boat,
even if flat-bottomed and of shallow draught of water, would run down the river-
course quicker than the water in which it swims ; for the reason that while all the
water surrounding it makes occasional visits to the bottom of the river, and meets
with great retardation there, the boat does not dive to the bottom, and is free from
any such retardation, and so is only held back by the surrounding water against
taking from gravity a perpetually increasing velocity. Thus it must go faster
than the surrounding water which has to hold it back. The boat of deeper draught
referred to by the committee I would suppose would advance quicker than the
surface water, for the same reason, and not merely because of its bottom being
situated in water moving quicker than that at the surface. The principles I have
assigned would afford ample reason for our supposing that the boat of deep
draught might swim forward much quicker not only than the surface water, but
also than the water at its bottom, or indeed than any part of the water of the river
surrounding the boat. Very small floating objects, such as sticks or leaves, would
present, in proportion to their small masses, so much resistance to motion through
the surrounding water that they would be constrained in fact to move sensibly at
the same velocity as that of the water surrounding them. The phenomenon would
thus be presented of the boat swimming forward past the small floating objects
around it. J. T.

120 PAPERS RELATING TO MOTION OF FLUIDS [19

water from the bed, such as it appears do commonly intrude into
the body of the current, there would be no retardative influence to
counteract the gravitational accelerative influence ; since the mere
viscosity of the water unaided by transverse commingling is, I
consider, insignificantly small and quite ineffectual as a resisting
influence or means of transmitting resistance from the bed to any
part of the water in the body of the current out of close proximity
to the bed. But as this forward moving water is also descending
towards the bottom while it is gaining forward velocity, it follows
that, in the circumstances of flow supposed, we ought to expect
the forward velocity to increase with descent from the Surface
to very nearly the bottom. It is to be understood that the
freedom supposed from upward rushes or intrusions of deadened
water will not be maintained in the water when it arrives into
proximity to the bottom. In approaching very near to the
bottom the water must begin to receive important resisting forces
communicated to it from the bottom through commingling of
deadened water, and by intense distortional actions with viscosity.
It is also to be noticed in connexion with the case under con-
sideration that if, in one part of the width of the river, there is
a prevailing descent towards the bottom, there will be upward
flows to compensate for this in other parts of the width. Then
obviously the whole character of the action of the water will be
very different in the regions where ascent prevails from that in
the regions where there is a prevailing descent; and the dis-
tribution of forward velocities throughout any vertical line in the
one region will be quite different from the distribution of forward
velocities throughout any vertical line in the other region. Local
circumstances casually affecting the flow in the way here described
I think may perhaps account for some of the apparent anomalies
in respect to the distribution of velocities through different parts
of the depth from surface to bottom which have been met with by
various experimenters, and have been included among the re-
cognised causes of the perplexity and bewilderment with which
this branch of hydraulic science is pervaded.

I wish next to draw attention to one of the results of observa-
tion and experiment announced by Captain Cunningham in his
book already referred to (Hydraulic Experiments at Roorkee). In
his discussion of his experimental results on the flow of water in
each of two artificially-formed channels on the Ganges Canal, one

1878] ON THE FLOW OF WATER IN UNIFORM REGIME 121

of them, 168 feet wide, and the other 85 feet wide, and each
having the water often about from 6 feet to 9 feet deep, he states
(p. 46, article 35) : " There is a constant surface motion (deviation)
from the edges towards the centre, most intense at the edges and
rapidly decreasing with distance from the edges."

This experimental conclusion, on the supposition of its being
decidedly trustworthy, as Mr Cunningham asserts with confidence
that it is, I think may probably be satisfactorily explicable through
considerations intimately connected with those which I have already
given for an amended theory of the flow of water in rivers.

I wish, however, not to prolong the present paper by entering
on any detailed discussion of this branch of the subject, and
besides I prefer to reserve this for some further consideration
before venturing to put forward the views in reference to it which
at present appear to me likely to be tenable. It may be noticed,
however, that Captain Cunningham's experimental result, if
decidedly correct, throws additional light on the subject of the
abatement of surface velocity comparatively to the velocity at some
depth below the surface being found in Bazin's experiments to
occur in a much greater degree near the sides of rectangular and
various other channels than at middle. Bazin thought indeed
from his own experiments (as I have already had occasion to
mention) that the relative retardation or slowness of the surface
occurred not in the middle of wide channels (that is to say, of
channels wide relatively to the depth of the water) but only near
the sides ; but this supposition I have referred to as appearing not
to be trustworthy. With these brief suggestions I will now leave
for further consideration the subject of the special phenomena of
the influence of the sides.

Historical Note.

Subsequently to my having formed, in all its primary or more
essential features, the new view now explained of the flow of water
in rivers, and before I had met with the book of Humphreys and
Abbot, I happened to see in the writings of another author (paper
of Mr Gordon already referred to) the following remark in reference
to their views as to the velocity at the surface being less than at
some depth below. " Humphreys and Abbot attribute the fact to
transmitted motion from the irregularities of the bottom; but
confess themselves dissatisfied with their own explanation."

122 PAPERS RELATING TO MOTION OF FLUIDS [19

These words seemed to me to indicate a probability of Humphreys
and Abbot having anticipated me in some part at least of the
theory which I had been forming. On obtaining their book, how-
ever, and reading the passage referred to, not by itself alone, but
with its context, it appeared to me that it involved no real
anticipation, although one clause of a sentence in it, read by itself,
might be supposed to do so. The passage is to be found in their
work at p. 286. They begin by saying, that their experimental
observations detailed in their previous pages " prove that even in
a perfectly calm day there is a strong resistance to the motion of
the water at the surface as well as at the bottom," and tliat this
resistance at the surface " is not wholly or even mainly caused by
friction against the air." They go on to say: — "One important
cause of this resistance is believed to be the loss of living force,
arising from upward currents or transmitted motion occasioned by
irregularities at the bottom. This loss is greater at the surface
than near it. The experiment of transmitted motion through
a series of ivory balls illustrates this effect. It is likewise illus-
trated on a large scale by the collision of two trains of cars on
a railway, in which case it has been observed that the cars at the
head of the train are the most injured and thrown the farthest
from the track ; those at the end of the train are next in order of
injury and disturbance; while those in the middle of the train are
but little injured or disturbed. Other causes may and probably
do exist, but their investigation has, fortunately, more of scientific
interest than practical value. For all general purposes it may be
assumed that there is a resistance at the surface, of the same
order or nature as that which exists at the bottom."

Now although this passage does contain the words "arising
from upward currents or transmitted motion occasioned by irregu-
larities at the bottom" yet the illustrations, by means of the series
of ivory balls, and of the collision of railway trains, show that the
authors attribute to those words no clear and correct meaning, but,
on the contrary, I would say they put forward quite a false view
of the actions going on. Besides I myself do not admit that,
except from the air, there is a resistance at the surface. According
to my supposition the already resisted and retarded bottom water
comes to the surface and spreads out there, but receives no new
resistance there, and on the contrary receives acceleration from
gravity in running down hill.

1888] FLUX AND REFLUX IN CHANNELS OR PIPES 123

20. ON FLUX AND REFLUX OF WATER IN OPEN CHANNELS

OR IN PIPES OR OTHER DUCTS.

[From the Philosophical Magazine for October 1888. Having been read at
the British Association, Section A, Bath, 1888.]

IN the autumn of 1872 I was staying at a place named
Castlerock, on the north coast of Ireland, between the mouth
of the Bann River and the entrance to Lough Foyle. There
was an extensive sandy beach there, lashed by the great waves
of the Atlantic Ocean. At a part of that beach a small river
or stream flowed to the sea; but the sandy beach had been
thrown up as a bank, at about high-tide level, obstructing what
might have been the direct outfall course for the stream into
the sea, and causing the stream to turn to its right and to flow
eastward for some distance along the back of that sandy bank
before finding an opening for flow out to the sea. Thus, at the
back of the bank, a little estuary was formed, along which, when
the tide was down, the stream would have for a considerable
length a nearly level bed; and into which, when the tide was
up, the sea-water entered so as to fill it up to various depths
according to the height of the sea-surface.

I happened to be watching with interest the motions of the
water in the little estuary at a time when a considerable depth
of water (such as a few feet depth along its mid-channel) was
maintained in it by the height of the sea-water outside, and
when the slow rising and sinking of the ocean-waves was
producing in the estuary a flux and reflux on a small scale
like that of the tidal flow in large estuaries*. The motions of
the water being indicated by numerous little pieces of sea-weed
carried in suspension, I noticed that the water at or very close
to the channel-bed reversed its landward or seaward flow always
much earlier than did the main body of the water in the
channel, less affected by contiguity to the bed. The phenomenon

* The period of these oscillations may be about from 10 to 20 seconds ; as I
have been informed that Prof. Stokes has found, by observations on that coast,
that the period from one wave to the next, in the large Atlantic waves there, is at
most about 17 seconds. [See Scientific Correspondence of Sir George Stokes, Vol. n.
p. 142 seq.]

124 PAPERS RELATING TO MOTION OF FLUIDS [20

being noticed, the reason at once became apparent. The lamina
contiguous to the bed, or channel-face, would be always hindered
by the frictional resistance of that face from getting into so
great a velocity, either seaward or landward, as that which would
be attained to by the main body of the water. Then, when the
water at the sea-end of the estuary was raised in level, by the
arrival of an ocean-wave, so as to give a gravitational propulsive
influence tending to cause the water to flow landward along the
estuary, the main body of the water, in virtue of its inertia
with seaward momentum, would continue to flow for some time
seaward, flowing as it were uphill*; while the frictionally restrained
lamina at the channel-face, being nearly devoid of inertial ten-
dency seaward, would readily yield to the landward gravitational
propulsive influence due to the landward surface declivity of the
water in the estuary.

Exactly a like explanation, mutatis mutandis, is applicable
to the case of reversal of the flow from having been landward
to its becoming seaward. The channel-face lamina makes its
reversal of flow, just as in the other case, earlier than does the
main body of the water, and for like reason.

It may now further be noticed that precisely corresponding
phenomena would present themselves in the flux and reflux of
water in a pipe; if, for instance, the pipe were connecting two
cisterns, and a plunger were kept oscillating upwards and down-
wards in one of them so as to cause the alternating flow through
the pipe. The phenomena might be very interestingly manifested
in an open trough connecting two cisterns, arrangements being
made, by a plunger or otherwise, for causing flux and reflux
along the trough, and the motions of the water being indicated
by small visible particles in suspension in the water, or by the
dropping in of granules of aniline dye.

It may now be worthy of remark that the hydraulic principle
brought into notice in the present paper, in respect to Flux and
Reflux along Channels, is closely allied to, and is in some respects
identical with, the leading principle set forth in previous papers
by myself on the Flow of Water round Bends in Rivers, &c.
In that case the frictionally resisted and retarded lamina in
contiguity with the channel-face, or bed, flows transversely (or

* Or, in more precise terms, flowing from a place of lower to a place of higher
free level.

1888] FLUX AND REFLUX IN CHANNELS OR PIPES 125

rather obliquely) across the channel towards the inner bank of
the bend, impelled inwards by gravitational propulsive influence
(that is, downhill as it were), while the main body of the stream,
flowing quicker in the bend, exerts centrifugal force outwards, or
tends inertially out towards the outer bank. The papers here
referred to on Flow of Water round Bends in Rivers, &c. are to be
found in the Proceedings of the Royal Society for May 1876* ; in
the British Association Report for the Glasgow Meeting, 1876,
Section A, page 31 of Transactions of the Sections ; in the
Proceedings of the Royal Society, 1877, No. 182, page 356f ;
and in the Proceedings of the Institution of Mechanical Engineers,
August 1879, p. 456J. Also some other important cases in which
like principles of fluid motion come into play (in Whirlwinds &c.)
are adduced in a paper by myself in the British Association
Report for the Montreal Meeting, 1884, Section A, page 641 §.

21. ON CERTAIN CURIOUS MOTIONS OBSERVABLE AT THE SURFACES
OF WlNE AND OTHER ALCOHOLIC LlQUORS.

[From the Philosophical Magazine for November 1855. Read at the British
Association, Section A, Glasgow, 1855, pp. 16, 17.]

THE phenomena of capillary attraction in liquids are accounted
for, according to th'e generally received theory of Dr Young, by
the existence of forces equivalent to a tension of the surface of the
liquid, uniform -in all directions, and independent of the form of
the surface. The tensile force is not the same in different liquids.
Thus it is found to be much less in alcohol than in water. This
fact affords an explanation of several very curious motionr ob-
servable, under various circumstances, at the surfaces of alcoholic
liquors. One part of these phenomena is, that if, in the middle
of the surface of a glass of water, a small quantity of alcohol or
strong spirituous liquor be gently introduced, a rapid rushing of
the surface is found to occur outwards from the place where the
spirit is introduced. It is made more apparent if fine powder be
dusted on the surface of the water. Another part of the phenomena

* [Supra, No. 16.] t [Supra, No. 17.]

J [Supra, No. 18.] § [Infra, No. 26.]

126 PAPERS RELATING TO MOTION OF FLUIDS [21

is, that if the sides of the vessel be wet with water above the
general level of the surface of the water, and if the spirit be
introduced in sufficient quantity in the middle of the vessel, or if
it be introduced near the side, the fluid is even seen to ascend the
inside of the glass until it accumulates in some places to such an
extent, that its weight preponderates and it falls down again. The
manner in which I explain these two parts of the phenomena is,
that the more watery portions of the entire surface, having more
tension than those which are more alcoholic, drag the latter briskly
away, sometimes even so as to form a horizontal ring of liquid high
up round the interior of the vessel, and thicker than that b$ which
the interior of the vessel was wet. Then the tendency is for the
various parts of this ring or line to run together to those parts
which happen to be most watery, and so there is no stable equi-
librium, for the parts to which the various portions of the liquid
aggregate themselves soon become too heavy to be sustained, and
so they fall down.

The same mode of explanation, when carried a step further,
shows the reason of the curious motions commonly observed in the
film of wine adhering to the inside of a wine-glass, when the glass,
having been partially filled with wine, has been shaken so as to
wet the inside above the general level of the surface of the liquid ;
for, to explain these motions, it is only necessary further to bring
under consideration that the thin film adhering to the inside of
the glass must very quickly become more watery than the rest, on
account of the evaporation of the alcohol contained in it being
more rapid than the evaporation of the water.

That this part of the explanation is correct, or that these
motions of the film in the wine-glass are really due to evaporation,
may be shown by a very decisive experiment. If a vial be partly
filled with wine and shaken, and then allowed to rest, no motion
of the kind described will be found to occur in the thin film wetting
the inside, provided that the vial be kept corked. On the cork
being removed, however, and the air contained in the vial, and
saturated with the vapour of wine, being withdrawn by a tube, so
as to be replaced by fresh air capable of producing evaporation, a
liquid film is instantly to be seen creeping up the interior of the
vial with thick or viscid-looking pendent streams descending from
it like a fringe from a curtain. These appearances are quite of
the same kind as those met with in the open wine-glass.

1855] TEARS OF STRONG WINE 127

Another experiment may be made to show, in a very striking
way, the phenomenon of the more watery portion of the surface
of a mixed liquid drawing itself away from the more alcoholic
portion as follows: — If water be poured to the depth of about
a tenth of an inch or less on a flat silver tray or marble slab,
previously cleaned from any film which could hinder the water
from thoroughly wetting its surface ; and if then a little alcohol
or wine be laid on the middle of that water, immediately the water
will rush away from the middle, leaving a deep hollow there, and
indeed leaving the tray bare of all liquid except an exceedingly
thin film of the spirit, which continues always thinnest close to
the margin of the water, because the water draws out to itself
every portion of the spirit which approaches close to its margin.

The experiment alluded to near the commencement of the
present paper, in which spirit was to be introduced into the
middle of a surface of water previously dusted over with fine
powder, may be well conducted as follows : — A tube for supplying
the spirit should be provided*, which may be three or four inches
long, half an inch or three-quarters in diameter, and terminating
at bottom in a small open point, which, if found too wide, may be
partially stopped by the insertion of a piece of thick soft thread,
such as a strand from the wick of a spirit-lamp. A knot on the
thread inside of the tube will serve as a valve to curtail or stop the
flow of the spirit when required. The surface of the water should
be clean and free from any kind of pellicle, such as is often met
with, and is sometimes not easily avoided. It should then be
lightly dusted over with some fine powder not apt to be quickly
wet : Lycopodium powder will serve the purpose. Then the tube
filled with spirit is to be dipped with its open point into the surface
of the water, and instantly a nearly circular patch round the point
of the tube will be seen occupied with liquid rushing outwards and
completely divested of the covering of powder, while on the part
outside of that patch there will be seen, by the motions of the
powder, one, two, three, or many radial streams flowing outwards
from the middle, and other return streams or eddies flowing back-
wards to the margin of the patch, on arriving at which each particle
seems suddenly as if driven outwards with a rapid impulse. The
margin of the central patch is usually to be seen formed like as of

* The tube of a small glass syringe as sold by apothecaries will serve the
purpose well.

128 PAPERS RELATING TO MOTION OF FLUIDS [21

leaves of a plant growing out all round, and some superimposed on
others, and all in rapid motion. The nature and causes of these
forms of the margin, and of the eddies outside of the margin, I
have not as yet been able satisfactorily to explain.

Another experiment may be made which is quite in accordance
with the explanations already given, and which, being due to con-
densation of alcohol on a surface of water, is interesting when
viewed in comparison with that in which the motions were shown
to be produced by evaporation : — If a silver spoon, perfectly wetted
with water so that a thin film adheres to it, be held over an open
cup or vessel containing strong alcohol, the surface of th^ liquid
will become greatly agitated with numerous motions, which are to
be attributed to the unequal and varying condensation of the
vapour of the alcohol at different parts of the surface of the film,
according as the vapour is wafted about in fumes by the air.

While engaged in the investigation of the phenomena which
I have now described, my attention has been turned to some other
very interesting phenomena previously observed by Mr Cornelius
Varley, and described by him in the fiftieth volume of the Trans-
actions of the Society of Arts. He observed, with the aid of the
microscope, numerous motions of extremely curious and wonderful
characters in fluids undergoing evaporation. Although I have not
yet had it in my power to examine into all the phenomena he has
discovered relative to these motions, yet I think that many of
them, or all, are to be explained according to the principles I have
now proposed.

I have not had access to the Transactions of the Society of Arts
to read Mr Varley 's paper in full, but I quote the following abstract
of his results from Queckett's Treatise on the Microscope, 1st ed.
p. 413 : — " The plan recommended is as follows : take an animalcule-
cage of moderate size, and upon the tablet place a drop of turpentine
or spirits of wine, &c.. then slide over it the thin glass cover, but
do not compress the fluid very much ; the microscope being placed
in the vertical position, and provided with a magnifying power
from 40 to 100 diameters, the contents of the cage are to be
examined in the same way as if animalcules were contained in it.
As the evaporation of either of these fluids takes place, numerous
currents and vortices will be seen, especially if a small quantity of
finely-powdered coal be ground into them; the particles of coal
being very light, are held in suspension whilst the evaporation is

1855] TEARS OF STRONG WINE 129

going on, and are whirled about by the currents in different
directions." The following fluids Mr Varley has given as the best
for the illustration of the currents : —

" 1. A drop of spirits of wine, or of naphtha, exhibits two,
three, or four vortices or centres of circulation, according to the
size of the drop; and if these vortices are viewed laterally, the
lines of particles will be seen forming oblique curves from top to
bottom of the drop.

" 2. Oil of turpentine shows a rapid circulation in two con-
tinuous spirals, one to the right, the other to the left, around the
drop. These meet in the opposite diameter, from which the
particles are carried slowly across the diameter to the place of
starting, and this continues while there is fluid enough to let it be
seen.

" 3. If, however, the drop does not exceed one-tenth of an inch
in diameter, it presents the appearance of particles continually
rising up in the middle, and radiating in gentle curves to the
circumference.

" 4. If the liquid be put into a very small vial, similar motions
are perceived, the particles when they have reached the side of the
vial going down to rise up afterwards in the centre or axis.

" 5. If a bubble of air be enclosed in the liquid, motions similar
to those described in No. 2 are observed in the part immediately
in contact with the bubble.

"6. In a flat drop of new wine laid on the tablet or disc of
the aquatic live-box, but not compressed by the cover, the motion
was a regular uniform circulation, the particles rising from below
at one end of the drop, then passing straight across on the surface,
and descending at the other end*."

* [See Clerk Maxwell, Theory of Heat, 4th edition, 1875, p. 293 : " This pheno-
menon, known as the tears of strong wine, was first explained on these principles by
Professor James Thomson. It is probable that it is referred to in Prov. xxiii. 31,
as an indication of the strength of the wine."]

T.

130 PAPERS RELATING TO MOTION OF FLUIDS [22

22. ON SMOKY FOGS.

[From Northern Whig of Feb. 17, 1868. Abstract prepared by the author.]

A PRIVATE meeting of the Belfast Natural History and Philo-
sophical Society took place at the Museum, on the evening of
Wednesday, the 12th inst. The President (Mr Joseph John
Murphy) occupied the chair.

Professor James Thomson read a paper on Smoky Fogs. The
question which he proposed to discuss was — How are we to account
for the well-known and frequently-noticed fact of the smokiness
of the air in towns often being excessively aggravated in times of
fog; or, at least, of the smokiness becoming often in such times
more perceptible and more disagreeable than usual ? He said it
cannot be that the chimneys give out more smoke then than at
other times, nor can it be merely that the air is then calmer than
usual, for we often have in towns cold, calm weather, with tolerably
clear or bright, fresh air. Also, it cannot be merely that the
smoke, with the fog super-added, appears more dark and thick
than usual, for when this foggy, smoky air comes into our well-
warmed houses, the fog is dissolved or dissipated by the heat;
but the smoke remains distinctly perceptible to an unusual degree
even within the limits of our warmed apartments. Neither could
he admit, what is frequently offered as an explanation, that the
smokiness in question is to be attributed to the particles of smoke
becoming, in foggy weather, loaded with moisture, so as to be
prevented from rising freely up and away from the streets and
houses. Last winter, he had noticed smoky fog accompanying
thaw after severe frost; and this not infrequent occurrence had
suggested to him an explanation, which he thought likely to
prove valid, for many, or perhaps all, cases of the phenomenon in
question. The rapid change often met with from frost to thaw,
and often even occurring in the night time, and without wind
at or near the ground, must be attributed to the arrival of a vast
mass or stratum of air from warm regions of the earth into the
space high above the ground, and above a bed of cold air previously
on the ground and still remaining there. The mingling of the
two masses of air at different temperatures tends, according to

1868] ON SMOKY FOGS 131

well-known laws, to produce cloud or mist at their junction. At
this stage, with a warm, cloudy sky, the thaw on the ground may
begin and advance rapidly. The moving current of warm air
above may continue till it has carried away nearly the whole of
the cold bed of air next the earth, so as to leave at the earth
only a stratum of the cloudy mixture of the previously warm
with the previously cold air. If, now, the forward motion of the
warm air gradually abates, and a calm condition of the atmosphere
ensues, we have at the ground, and among the streets of a town,
a bed of air which is cold and consequently heavy, and which is
also foggy; while the atmosphere immediately above is warmer
and lighter. The coldest and heaviest air, being at the bottom,
tends to stagnate down about the houses ; all upward and down-
ward currents, such as might often at other times occur, being
then arrested. Thus, in the stagnating lower stratum, the smoke
emitted as usual from chimneys accumulates excessively, accom-
panied by the fog due to the cooling of the lower part of the
newly-arrived, warm moist air.

[The following MS. note by the author is dated Nov. 28, 1870:]

I find in Herschel's meteorology, published separately from
Encyclopedia Britannica, 1862, page 98, that Herschel attributes
the dense yellow suffocating fogs which infest London, especially
in the winter months, to the sooty particles acting as nuclei of
radiation and causing the fog.

I do not think the explanation offered by Herschel can be
tenable. Without seeing the phenomenon he alludes to I could
not attempt decidedly to explain it. He says : — "A very peculiar
phenomenon exhibited by the London atmosphere has been de-
scribed to us by the Astronomer Royal and appears to be referable
to the same cause. On calm evenings after sunset, as seen from
the Royal Observatory on Greenwich Hill, the vast irregular mass
of smoke hovering over London appears to subside. Its heaped
and turbulent outline becomes flat and sinks rapidly into a low
level cloud bank, with a very definite outline, and fair sky above.
It would seem that each particle of soot, acting as an insulated
radiant, collects dew on itself, and sinks down rapidly as a heavy
body."

Now I presume the turbulent outline is really the result of
many ascending and descending currents due on the calm day to
the heat of the sun warming the town and warming the smoky

9—2

132 PAPERS RELATING TO MOTION OF FLUIDS [22

air; but that after sunset this cause of upward and downward
currents soon ceases to act : — and I suppose it very likely that
radiation from the air and soot etc. may cool the low stratum
after sunset and cause it to lay itself down flat: — but this flattening
I think must be due much more to a subsidence of a heavy cool
stratum of air with included smoke than to the falling of heavy
dew-bemoistened particles of soot out of the air where they were
to a lower mass of air so as to clarify by precipitation of soot the
sooty air. I think also it may be well to keep it an open question
whether the "very peculiar phenomenon" referred to by Herschel
may not sometimes or in some degree be due to the supervention
of a flow of warmer air above the smoky atmosphere : though
I think this scarcely likely to account for the phenomenon
described. At present it seems to me most likely that the sooty
particles in the air would radiate heat out to the cold sky, and
that they, by becoming cooled, would cool the air surrounding
them, and that the air thus becoming heavier would sink, and that
its tendency to sink would be increased by the weight of the soot
and of the dew attached to it if such there be ; but I think the
main levelling action must be that of a cooler and denser fluid
spreading itself out flat below a warmer and lighter one (very like
the self levelling of syrup at the bottom of a vessel of water) and
I distinctly think the precipitation of sooty particles from air
containing them cannot possibly account for the phenomenon
described. I think they could not go down so as to leave clear
and transparent the air which contained them. The turbulent
roughnesses would be, I am sure, 50, 100, 500 or more feet high ;
and it is inconceivable that any such masses of air could clarify
themselves, by precipitating their soot down through themselves
and out of themselves. The different sized pieces would fall at
different rates and the finest particles of smoke, I suppose, would
not descend in the whole course of an evening so as to clarify a
stratum 10 ft. deep. The smoke of a smoky fire in a dwelling
room will last a long time without settling by precipitation. It
is usually got rid of out of the air mainly by ventilation though
partly by precipitation. Now over London it is quite conceivable
that sometimes after sunset the smoky air may become cooler
than before, by radiation ; and that through various causes (the
passage of a barometric wave for instance perhaps, etc. etc.) a
stratum of warmer and lighter and purer air above may be slowly

1868] ON SMOKY FOGS 133

depressed, while the smoky turbulent mass flattens itself down
while gently gliding out sidewise from London. Some such
action as that, I think, would account for the sinking of the
turbulent smoky canopy to a smoothed and lowered sheet and
for vision being free at a level which was smoky before. Probably
too there would be a gentle wind, not a perfect calm in the air
high up, and thus new pure air would replace some lofty air slightly
vitiated with smoke.

23. ON SMOKY FOGS. (Second Paper.)
[From Northern Whig of Dec. 6, 1870.]

THE third joint meeting of the [Belfast] Natural History and
Philosophical Society and the Naturalists' Field Club, for the
session 1870-71, was held in the Museum, on Wednesday evening,
the 30th November. The chair was occupied by the President
of the Natural History and Philosophical Society, Robert
Patterson, F.R.S. Dr James Thomson offered some remarks on
Smoky Fog.

Many persons in Belfast will remember having noticed the
air in their houses on Saturday evening last, the 26th of November,
as being in an excessively smoky condition. People in many
cases at first thought the smoke pervading their apartments and
staircases was coming from some of the fires within their own
house. But this idea was dispelled when they found their
chimneys drawing just as well as usual; and the truth became
apparent that Belfast was enveloped in a densely smoky fog. It
cannot be supposed that the fog itself could continue to exist in
the air after entrance into the well-warmed apartments in houses,
as it would instantly dissolve away under the influence of the
warmth ; but certainly the smoke remained most disagreeably
evident, apparent to the eyes, and perceived almost suffocatingly
in the throat. At that time on a Saturday evening the mill
chimneys must have ceased to emit their usual smoke, and the
dwelling-houses would be only giving off about their usual
quantity. What, then, could be the reason why the air of the
town should at that particular time be ten-fold, fifty-fold, or,
perhaps, a hundred-fold as smoky as usual ? Mere calmness of
the atmosphere would not suffice to account for such excessive

134 PAPERS RELATING TO MOTION OF FLUIDS [23

smokiness, because often we have in towns calm weather with
very tolerably clear air, fresh and pleasant. He thought the
explanation of the phenomena in question was afforded by a
theory which he had submitted to the Natural History and
Philosophical Society in February 1868. The view he then gave,
and which he thinks meets with confirmation from the atmospheric
phenomena of Saturday and Sunday last, was to the effect that
the usual or general cause of excessively smoky fogs is the arrival
in the sky over a town of a vast influx of warm air, much warmer
than the air lying calmly on the ground and immediately over
the houses. The mingling of the two masses of air at different
temperatures must tend, according to well-known laws, to produce
cloud or mist at their junction, especially if both, although clear,
be nearly saturated with moisture in the gaseous state. If the
substratum of cold air be of considerable depth, the first indications
of the arrival of the warm air may be a clouding of the sky, and
a rise of temperature at the ground due to radiation of heat
downwards from the newly arrived air, the warmth at the ground
often in such cases showing itself by an incipient thaw if there
has been frost before. Then as time advances, the cold substratum
may be gradually thinned away by the scouring off of its upper
part by the current of warm air flowing above it, till the foggy
junction where the intermixture is proceeding extends down to
the houses and the ground. In this way there may be brought
about a condition in which the lowest air will be the coldest,
and in which there will be a gradual increase of temperature in
ascending for a considerable height from the earth upwards. If
now the newly arrived warm air maintains a brisk flow, there
certainly will be no smoky fog, because the smoke will be carried
away as quickly as it is evolved from the chimneys. But if, with
the distribution of temperature already supposed to have been
attained, a calm supervenes, we have a set of conditions present
together which can scarcely fail to produce a smoky fog, because
the coldest and heaviest air, being at bottom, must tend to stagnate
there, all upward and downward currents, such as often at other
times occur, being then arrested. Thus in the stagnating lower
stratum the smoke emitted as usual from the chimneys must
accumulate excessively; and if the newly arrived warm air be
moist enough to produce fog by its mixing with the cooler air
below, as must often be the case, the accumulating smoke will be

1870] ON SMOKY FOGS 135

accompanied by fog, and so the smoky fog will be produced. If
the newly arrived air over the substratum of colder air be warm
and not very moist, an excessive accumulation of smoke may occur
in the atmosphere of a town in calm weather without there being
necessarily any fog, the main conditions tending to an extra-
ordinary accumulation of smoke being a calm atmosphere, with a
cool stratum at bottom, and warmer air above, and with the cool
stratum extending high enough to cover the chimneys of a town,
and receive their smoke. On the other hand, if the upper air be
cool, having recently come from some cold region of the earth,
and the lower air be warm, as it often may be when the sun is
shining on the ground and on houses and streets, the air of the
town may be kept clear and fresh without any perceptible wind
by a constant gentle interchange of air upwards and downwards,
the warm air of the town floating upwards and being replaced by
the cool air from above. Last Saturday was a sunny, frosty day
in Belfast and the neighbouring country. The frost was not
severe, as some parts of the roads were wet, while others were
hard frozen. In gardens in the town sheltered from the sunshine
there was hoar frost on the leaves, and water exposed had a crust
of ice. During the day time the air was more or less foggy in
various parts of the town, and some appearances of unusual
sinokiriess were observed also. The frost continued till after
sunset. In the evening, at about 6, 7, 8, and 9 o'clock, the town
was enveloped in an intensely smoky fog ; and the smokiriess of
the air was very unpleasantly perceptible even in well- warmed
rooms in which the fog itself would be completely dissipated.
This condition of things, then, when considered under the theory
already explained, appeared to prove that a vast mass of warm
moist air had arrived aloft, while a cold stratum of air was still
left stagnating below and enveloping the town. The surmiac
that such must be the case was made on the Saturday evening,
and was abundantly confirmed on the following morning; for,
on the Sunday morning, the frost was all gone, the smoky fog
was gone, and the air was remarkably mild, and moist, though
clear, and there was sunshine during much of the day, and the
stars were visible in the evening. The occurrence of the thaw
and warmth in the night time, when no sun was shining,
affords strong proof of the influx of warm air having really taken
place. In fact, all the previous cold air in which the smoke had

136 PAPERS RELATING TO MOTION OF FLUIDS [24

accumulated was carried away during the night time, and the
town was enveloped with newly arrived air from some warmer
region of the earth. The warmth and moisture of the air were
clearly shown by copious deposition of condensed vapour which
was to be seen trickling down the surfaces of painted stone
columns and other large non-absorbent objects which had been
exposed to the cold of previous days.

24. ON A CHANGING TESSELATED STRUCTURE IN CERTAIN
LIQUIDS [DUE TO CONVECTIVE CIRCULATION*]. v

[Abstract of Paper read to the Philosophical Society of Glasgow,
Proceedings, 15th February, 1882.]

IN June, 1870, the author, when on an excursion of the Belfast
Naturalists' Field Club, happened to notice in a tub of opaque-
looking water, in the yard of a roadside inn, a structure showing
itself, which appeared remarkable, and excited a good deal of
curiosity among members of the Club then present, as to what
might be its nature and mode of origin. The water, viewed from
above, presented a tesselated appearance, considerably resembling
such patterns as are exhibited by vertical basaltic columns when
exposed to view in a horizontal section — such, for instance, as may
be seen at the Giants' Causeway or at StafTa. On the water being
disturbed the tesselated structure was destroyed, and eddying
streams of pearly lustre showed themselves in its stead ; but the
same kind of tesselated structure as before, speedily reappeared,
and, on being watched for some time, it was found to be perpetually,
though slowly, changing. Inquiries made as to how the water
had been previously used did not elicit any definite information.
A sample of the water was then brought away by the author for
further examination. It presented, when shaken in a clear glass
bottle, a remarkable satin-like, streaky appearance, with the pearly
lustre before mentioned.

Like phenomena were afterwards noticed occasionally in soapy
water, and so it became probable that the water originally noticed

* [This subject has been investigated independently and with extensive de-
velopments by Prof. Benard of Bordeaux in a Thesis published in the Annales de
Chemie, 1901 (cf. also a note by him in the forthcoming part, Dec. 1911, relating to
the present paper) : see also Benard, Eevue Generate des Sciences, 1900; and also in
connexion with Solar phenomena, Deslandres, Annales de Meudon, Vol. iv. 1910.]

1882] ON A CHANGING TESSELATED STRUCTURE IN LIQUIDS 137

might have been soapy, and that soapyness had probably been
associated with the production of the phenomena.

Various experiments and observations on soapy water have
since been made, and results which seem worthy of notice have
been arrived at. The more obvious features of the phenomena
must of course have been seen thousands of times before by
washerwomen and others; but perhaps the conditions may have
been left unheeded, and without receiving any scientific attention
or scrutiny.

The occurrence of the phenomena seems to be associated
essentially with cooling of the liquid at its surface where exposed
to the air, when the main body of the liquid is at a temperature
somewhat above that assumed by a thin superficial film. A very
slight excess of temperature in the body of the fluid above that
of the surrounding air is sufficient to institute the tesselafced
changing structure, provided that the soapy water is in other
respects in good condition for taking the actions to which the
phenomena are due.

An easy method of procedure for making suitable experiments
and observations, and which was shown to the Philosophical Society
in illustration of the communication, will now be explained. A
glass pan was filled to a depth of four or five inches with soapy
water of proper consistency, arrived at by previous trials. Then,
to warm it slightly, one or two small tin cans of hot water were
plunged into the soapy water, so that heat would be given to the
soapy water by conduction through the sheet metal. The warm
water cans were then removed, and the soapy water was stirred
to bring the whole to about a uniform temperature. Then the
pan and its contents were left undisturbed, and the subsequent
behaviour of the liquid was watched. Swirling flows, conspicuous
by their pearly streaks, showed themselves for some time, but with
gradually abating speed, and in the course of five or ten minutes
the eddying motions, accompanied by spirally-formed moving
streaks, were gradually dying out, and the moving patterns on the
surface were, by slow degrees, assuming a tesselated character.
After the cessation of all such swirling motions, and disappearance
of spirally-moving streams, the tesselated configuration might be
found to continue, perpetually changing in all its individual details
from minute to minute, but retaining the same general character
for many hours together.

138

PAPERS RELATING TO MOTION OF FLUIDS

[24

Fig. 1 represents the general appearance that the surface
of the soapy water in the pan would usually exhibit when
left standing in the manner described. By continuous watching,
it may be noticed that the smaller enclosed patches are generally
diminishing in size, being encroached on by the larger ones until

Fig. 1.

they collapse and cease to exist. At the same time the large ones
show tendencies to sever themselves into two or more new ones,
which in their turn either increase and split again, or diminish
and go out of existence. To describe the numerous and varied

Fig. 2.

features of transition in words would not be easy, but figures 2,
3, and 4 show three successive conditions which have been observed
as occurring.

In fig. 2 the patch A has larger neighbours — B, C, D,

1882] ON A CHANGING TESSELATED STRUCTURE IN LIQUIDS 139

and E — contiguous with it, and it has also two narrow patches
— F and G — contiguous with small portions of its boundary.
The patch A is comparatively narrow in the direction between C
and E, and is rapidly encroached on by those two large patches G
and E, and becomes narrower than before, without necessarily being
shortened in length. Also, during the same time, the narrow
patches F and G collapse, each at its place of meeting with the
boundary of A ; and in each case where the collapse takes place a
bounding line is left between the two, which come together, as is
shown by mn and pq in fig. 3, the patches F and G of fig. 2
having retired to their new positions, shown as F and G in Fig. 3.
A little later, and the patch A is observed to have disappeared
entirely, by collapsing into the line st in fig. 4.

Multitudinous varieties of changes, partaking more or less of
the general character of those here described, may be noticed in

Fig. 3.

Fig. 4.

various watchings of the behaviour of the soapy liquid from time
to time. The patches, with their boundaries, when viewed with
favourably applied light, show appearances as if each patch were
formed as the top of a column of slowly rising fluid, having a
mother-of-pearl-like lustre, seemingly at a little distance below the
surface of the liquid, and with a thin layer of more translucent
liquid lying on the tops of these pearly patches. It seems to be
that there is on the whole a very slow ascending motion in these
columnar spaces, and that above, there is a thin superficial layer of
cooler and seemingly more translucent liquid, receiving perpetually
new supplies from the rising substance of those columns, and
flowing outwards over each column top, and that the two sheets,
spreading out on each of two contiguous columns, plunge down-
wards, where they meet in the mutual bounding line of the two
spaces or column tops, and so form a descending current or septum

140 PAPERS RELATING TO MOTION OF FLUIDS [24

between the two columnar spaces. Where three of the bounding
lines meet at the junction of three column tops, the downward
current seems to be more active than at the other parts of the
septums. The various ascending flows here spoken of as columns,
or columnar spaces, for want of any better nomenclature, may
probably not exist like separate columns with septums between
them of descending liquid except near the surface. It seems
likely that the down-flowing liquid of the so-called septums may
tend to gather into thicker streams descending from the corners
of the surface patches where three of such spaces meet ; but the
internal motions, being concealed from view, remain as yet obscure,
and in a great degree unknown.

Scrutiny of such motions as have here been briefly mentioned
and speculated upon has been carefully made in many ways, but
the one which gave the most remarkable indication was by
sprinkling minute crumbs of dry aniline dye on the surface of the
liquid, and observing the motions of the liquid, as indicated by
long worm-like coloured lines, which, as it were, crept forward
from the crumbs of the aniline, these crumbs themselves remaining
stationary, or nearly so, on the surface of the liquid. The blue
worms of aniline glided along the pearly tops of the columns,
sometimes forming a pit or depression, down which they would
plunge, accompanied by some of the cooler surface liquid; but
often they continued their course, so as to reach a bounding
septum, down which they could be seen to plunge rapidly. They
gave very clear indication of there being a down-flow of the
cooler surface liquid in every septum.

As to the physical and optical conditions to which the pearly
appearance may be due, the author offered some suggestions, but
stated that much must remain still to be found out by microscopical
or other researches, which he inclined to recommend to any whose
opportunities and inclinations might lead them to take interest in
the prosecution of such researches. He thought it probable, judging
from numerous appearances, that the soapy liquid might contain
in suspension multitudinous flattened or elongated particles, like
scales or crystals, or comminuted glass hairs, which, in the motions
and distortions of the liquid, would tend to place their flat faces
or their elongated sides in approximately-parallel directions, and
so would give special optical effects by their reflexion of light.
He offered any such suggestions, however, with great diffidence,

1882] ON A CHANGING TESSELATED STRUCTURE IN LIQUIDS 141

wishing to leave the subject entirely open for better researches
than any he had had opportunity to attempt.

A like tesselated formation, but without the pearly lustre, is
often to be noticed in a plate or bowl of beef-tea or other clear
soup containing minute flocculent particles in suspension and left
cooling. The flocculent particles are capable of showing the tesse-
lated structure, and of indicating clearly the existence of motions
such as those described as operative in the formation of the tesse-
lated structure in soapy water, but such particles are not capable
of reflecting the light so as to produce the pearly lustre.

The motions now described and explained as occurring in the
soapy water and other liquids when showing the tesselated
structure he thus believes constitute one special case of what is
often called convective circulation. He points out, however, that
this case, with a thin film cooled at the surface while the great
body of the liquid is at a somewhat higher temperature, presents
essential distinctions from the case in which convective cir-
culation is caused by heat applied at the bottom of the vessel.
The surface phenomena and the actual motions throughout the
body of the liquid are very different in the two cases, as may
easily be seen by a little consideration, both theoretical and.
observational.

Professor Thomson followed up the communication described
in the above abstract, by giving to the Society an account of views
which, a good many years ago, had been developed, partly by his
brother Sir William Thomson, and partly by himself, on a some-
what kindred subject — Calm Lines on a Rippled Sea. Those
new views he had submitted to the Belfast Natural History
and Philosophical Society in a paper read on 7th May, 1862,
of which an abstract is to be found in the Philosophical Magazine
for September 1862*. (Fourth Series, Vol. xxiv. page 247.)

The phenomena in the two cases — those of the Tesselated
Changing Structure, and of the Calm Lines on a Rippled Sea,
present certain features of close resemblance, and other features
of wide distinction ; and to facilitate the consideration of the two
subjects together, an abstract of the paper on the Calm Lines is
here subjoined.

* [Infra, p. 142.]

142 PAPERS RELATING TO MOTION OF FLUIDS [25

25. ON THE CAUSE OF THE CALM LINES OFTEN SEEN ON
A RIPPLED SEA.

[From the Philosophical Magazine, Fourth Series, Vol. xxiv. (1862), pp. 247,
248. Read before the Belfast Natural History and Philosophical Society,
May 7, 1862, and also printed in its Proceedings.]

IN this paper the object of the author was to offer a new
explanation of the origin of lines of glassy-calm water, usually
long and sinuous, which are often to be seen extending over the
surface of a sea darkened elsewhere by a ripple. He adverted to
the commonly received supposition that these lines are due to
some kind of oily film on the surface of the water, and to the
prevalent idea that the oil is somehow given off from shoals of
fishes. These suppositions, he thought, although having some
slight foundation in the facts of the case, did not form the true
explanation of the phenomenon. His brother, Professor William
Thomson, had observed, and had pointed out to him, that the
water at the calm lines always contains considerable quantities
of small floating objects, such as little detached pieces of seaweed,
leaves of trees, or the like, and had accounted for the smoothness
of the water by the friction induced among the little undulations
by the presence of those solid objects. The question still remained,
however, as to what might be the cause of the leaves and seaweed
being arranged in such long and sinuous lines. One of these
calm lines was noticed last autumn in Brodick Bay by Professor
William Thomson and the author; and on rowing into it, they
found leaves and seaweed abundantly diffused through the water
there, while the rippled water on both sides of it was comparatively
free from such objects. The line of calm water evidently sprang
from a point on the shore where a small river entered the sea,
and there could be no doubt that the leaves were supplied by
that river. Still it appeared an untenable supposition that the
river water could extend so very far out to sea, and wind about
over the surface of the sea as the calm line did, sometimes even
narrowing instead of spreading out as a broad sheet, which the
light fresh water flowing over the heavy salt water should be
expected to do. It occurred to the author that the water of the
river would actually spread out as a broad sheet over the surface
of the sea; and that in its outward lateral flow it would constantly

1862] ON THE CALM LINES OFTEN SEEN ON A RIPPLED SEA 143

be carrying with it the leaves with which it was originally charged,
and all such small pieces of seaweed as it might meet with in the
sea-water, and that these would accumulate in a boundary line of
the region of dispersion, which might be determined by some
slight flow of the surface of the adjacent sea- water meeting this
outspreading fresher water, and causing a downward or sinking
motion, however slight, of the two meeting currents. The author
does not mean to attribute the calm lines in general to the
spreading of a sheet of fresh water over the salt water of the sea,
but he thinks the general explanation is readily developed from
the observations and explanation in the foregoing particular case.
He supposes in general that in estuaries and channels of the sea,
and in lakes and rivers, the water must often be affected by
various causes, such as tides, breezes, currents, and circulation
due to differences of heat, so as to be made to rise occasionally
at some places and to sink at others. Now along the line of
meeting and sinking of two opposing surface currents, all floating
objects carried by those currents will be collected together; and
there they will act as dampers, or floating breakwaters, for the
small ripple undulations. The slightest possible inequalities of
the forces of the two opposing currents will suffice to account for
the great sinuosities which the calm lines show. If there should
happen to be any oily scum thinly diffused on the surface of the
water, this will be brought together, along with seaweeds, etc.,
from a wide area, to the line of meeting and descent of the two
opposing surface currents; and to an oily film having been
frequently noticed on the calm places, though really brought to
them in the way now suggested, the author inclines to attribute
the supposition that it is their cause; but he agrees that very
possibly, too, an oily scum thus sometimes brought together may
cooperate with the seaweed and other floating objects in resisting
the propagation of the ripple.

In the discussion which followed the reading of this paper,
it was remarked by members of the Society that, in drawing nets
through the sea near its surface for collecting small marine
animals, they had often found that these creatures were present
in vastly greater abundance in the calm lines than in the rippled
sea ; and it was suggested that, as the bodies of many of these
contain oil, this, on their dying, might be given off from their
bodies, and might float on the surface, and might cause the

144 PAPERS RELATING TO MOTION OF FLUIDS [26

smoothness there observed ; and it was also stated that shoals of
herrings are much more abundantly met with under the calm
lines than at other parts of the sea.

The author of the paper, in replying, pointed out that, if
marine animals giving off oil from their bodies were really the
cause of the calm lines, it would still remain as an unsolved
question, and one whjch would then be of great interest, Why
should those animals be found to congregate in long sinuous lines,
extending often continuously for miles over the surface of the
sea ? He thought, however, that the true state of the case would
probably be, that the small animals are brought together* by the
same currents which, according to his supposition, collect the
seaweed, leaves, and other floating objects into lines, and. that the
animals, not wishing to descend with the meeting currents into
deep water, remain near the surface, and that the herrings or
other fishes congregate to the same lines in order to feed on the
smaller animals.

26. ON THE GRAND CURRENTS OF ATMOSPHERIC
CIRCULATION.

[From MS. notes of a paper read to the British Association, Dublin, 1857.]

THE prime mover of atmospheric currents is the heat of the
sun, and the general or grand currents constituting the cir-
culation of the atmosphere originate in the difference of
temperature of the equatorial and polar regions. The currents
resulting from this source of motion are, however, greatly
influenced by the motion of the earth on its axis; or, in other
words, they are very different from what they would be if the
earth were at rest and if the sun were merely a source of heat
revolving round the earth according to its present apparent
motion.

To the combined agency of the equatorial heat and the
rotation of the earth the origin of the Trade Winds has been
long ascribed, and in this respect the ordinarily received theories
of the winds appear to me perfectly satisfactory. The same
agencies have also been taken into consideration with more or
less correctness to explain the prevailing motion from the west
in temperate and polar regions. I am not aware, however, that

1857] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 145

any satisfactory theory has as yet been promulgated showing the
nature of the atmospheric circulation except in, or about, the
Torrid Zone ; and to supply what appears to be wanting in this
respect is the object of the present paper.

In proceeding to explain my theory of atmospheric circulation,
I assume first as a well ascertained fact, that round the earth,
at or near the equator, there is a zone of air ascending in virtue
of its lightness produced by expansion by heat. This air, on
rising to the upper regions of the atmosphere must divide into
two great currents floating away from the equatorial zone towards
the poles. For the sake of simplicity of expression, I shall now
confine attention to the great currents of the northern hemisphere.
It is then to be observed that the air floating away in the upper
regions of the atmosphere from the equatorial ascending zone is
possessed of the rapid motion of rotation from west to east which
pertains to the equatorial regions of the earth in virtue of their
great distance from the earth's axis. The velocity of this motion
of rotation amounting as it does to a movement once round the
equatorial circumference of the earth in 24 hours may be stated
in round numbers at 1000 miles per hour. Endued with this
velocity at the outset, the great current floating away towards
the polar regions, comes successively into latitudes each having a
less velocity of rotation of the earth's surface than the preceding
one. The air then, tending to retain its original equatorial
motion from west to east, which, at the equatorial zone, was the
absence of motion in reference to the earth below it, comes by
degrees to have a rapid motion from west to east relatively to the
earth below it, in virtue of the velocities of the earth's surface
becoming less and less as the latitude increases. The air, of
course, is not to be understood as retaining its equatorial motion
of 1000 miles per hour undiminished in its course northward, for
it meets with retardation communicated upwards to it from the
slower moving regions of the earth's surface, through the medium
of the air below. For the present purpose it is necessary to refer
to this retardation merely with a view to show that there will
not be maintained such a powerful vortex or whirling movement
as would, by centrifugal force, hinder the motion towards the
higher latitudes. This motion towards the pole, accompanied by
a motion from west to east, quicker than that of the earth in
each latitude, in my theory I suppose to go on throughout the

T. 10

146 PAPERS RELATING TO MOTION OF FLUIDS [26

entire of the upper stratum of the air extending from the
equatorial rising zone to the cold regions of the north ; and the
grand current from equatorial to polar regions I suppose to occur
in the upper regions alone.

The cold of the polar regions increasing the density of this
air gives it a tendency to descend, and it does descend, and flows
as a grand under current towards the equator to take the place
of other air ascending in the equatorial rising zone, and in its
turn to rise in the same regions and repeat the circulation which
has now been briefly described. Throughout the regions extending
from about the 30th parallel of latitude northward, winds from
the west are observed to prevail, and those are to be ascribed to
the equatorial motion still remaining in part in the air when it
descends to the earth, and only to be removed by friction and
impacts against the earth's surface.

It is obvious that, as great a torsional force or couple must
be applied in these regions of west winds in retarding the
equatorial motion, as was applied in the equatorial regions in
generating that motion, and hence may be derived some con-
ception of the necessarily great extension and prevalence of these
west winds.

At latitude 30° the atmosphere on the surface of the earth
is found to have no average motion from west to east nor from
east to west : and it follows that, in passing from that latitude
to the equatorial rising zone, the air must fall behind the earth
in respect to rotatory motion ; or, in other words, the air will
revolve from west to east slower than the earth does, or will have
a motion from east to west relatively to the earth. This constitutes
the north east trade wind.

There is, however, a very important motion of the air, distinct
from the primary circulation which I have now described. It is
an observed prevailing motion of the winds on the earth's surface,
from south to north in the region occupied by the west winds.
This motion has generally, I believe, been considered as rather
paradoxical, and no explanation that appears to me to be tenable
has hitherto been proposed ; but, on the contrary, in Maury's
Physical Geography of the Sea, a recent and highly valuable work,
a theory of atmospheric currents is put forth, comprising this
motion as one of those that must be explained, and in that view
assuming a grand action in the upper regions of the atmosphere,

1857] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 147

which I look on as the contrary of what must really occur, and
as seeming so paradoxical that I can scarcely conceive of its being
satisfactory to any mind.

(Here show Maury's diagram*: give explanation as in Maury,
pp. 72, 73.)

Instead of this explanation I suppose the primary circulation
I have already described to occur in reality. Thus the atmosphere
over the temperate and frigid zone must be considered as in the
condition of a great vortex or whirl, the air revolving quicker
than the earth. Thus a partial vacuum or a diminished pressure
in the polar region must arise from the centrifugal force of the
whirling air. The film or stratum of this vortex however, which
is in contact with and in immediate proximity to the earth, must
have its rotatory motion retarded by friction and impacts on the
earth's surface.

Thus its centrifugal force comes to be less than that of the
great mass of atmosphere above it. It is therefore not aided by
centrifugal force so much as the parts above are in keeping out
from the polar region of diminished pressure, and consequently it
is actually drawn in by the vacuum towards the centre of the
vortex or in other words it receives a motion towards the pole of
the earth. Thus then does the friction of the earth's surface
serve to explain clearly and simply the motion towards the pole
which otherwise would appear paradoxical and which has led to
the supposition of such complicated and inexplicable currents as
have been supposed by Maury to occur.

[The foregoing is printed from MS. in the Author's hand.
The abstract of the paper in the Report of the British Association
proceeds as follows : — ]

This is the substance of Mr Thomson's theory ; and h- • gives,
as an illustration, the following simple experiment : — If a shallow
circular vessel with flat bottom, be filled to a moderate depth
with water, and if a few small objects, very little heavier than
water, and suitable for indicating to the eye the motions of the
water in the bottom +, be put in, and if the water be set to
revolve by being stirred round, then, on the process of stirring
being terminated, and the water being left to itself, the small
particles in the bottom will be seen to collect in the centre. They

* [For Diagrams see No. 28 infra.]

t A few tea-leaves taken from a teapot will suit the purpose well.

10—2

148 PAPERS RELATING TO MOTION OF FLUIDS [27

are evidently carried there by a current determined towards the
centre along the bottom in consequence of the centrifugal force of
the lowest stratum of the water being diminished in reference to
the strata above through a diminution of velocity of rotation in
the lowest stratum by friction on the bottom. The particles being
heavier than the water, must, in respect of their density, have
more centrifugal force than the water immediately in contact with
them ; and must therefore in this respect have a tendency to fly
outwards from the centre, but the flow of water towards the centre
overcomes this tendency arid carries them inwards ; and thus is
the flow of water towards the centre in the stratum in cbntact
with the bottom palpably manifested.

27. WHIRLWINDS AND WATERSPOUTS.

[From Nature, Oct. 30, 1884, Vol. xxx. p. 648. Read at the British
Association, Montreal, 1884. Printed in Transactions, p. 641.]

WHIRLWINDS, whether on sea or on land, have their characters
in great part alike. For simplicity it will be convenient to begin
by taking up only the case of whirlwinds on sea, as thus the
necessity for alternative expressions to suit both cases, that of sea
and that of land, will be avoided.

It may be accepted as a fact sufficiently established, both by
dynamic theory and by barometric observations, that at the sea-
level the pressure of the air is less in the neighbourhood of the
axis of whirl than it is at places farther out from the axis, though
within the region of the whirl. The apocentric force (centrifugal
force) of the rapidly-revolving air resists the inward pulsive
tendency of the greater outer than inner pressure. But close
over the surface of the sea there exists necessarily a lamina of
air greatly deadened as to the whirling motion by fluid friction,
or resistance, against the surface of the sea ; and all the more so
because of that surface being ruffled into waves and often broken
up into spray. This frictionally-deadened lamina exerts, because
of its diminished whirl speed, less apocentric force than the quicker-
revolving air above it, and so is incapable of resisting the inward
pulsive tendency of the greater outer than inner pressure already
mentioned. Hence, while rushing round in its whirl, the air of
that lamina must also be flowing in centre-ward.

1884] WHIRLWINDS AND WATERSPOUTS 149

The influx of air so arriving at the central region cannot
remain there continually accumulating; it is not annihilated,
and it certainly does not escape downwards through the sea.
There is no outlet for it except upwards, and as a rising central
core it departs from that place. This is one way of thinking
out some of the conditions of the complex set of actions under
contemplation ; but there is much more yet to be considered.

Hitherto, in the present paper, nothing has been said as to
the cause or mode of origin of the diminished barometric pressure
which, during the existence of the whirlwind, does actually exist
in the central region. Often in writings on this subject the
notion has been set forth that the diminished pressure is caused
by the rapid gyratory motion of the whirling air ; but, were we
to accept that view, we would have still to ask, How does the
remarkably rapid whirling motion receive its own origin ? The
reply must be that the view so offered is erroneous ; and that, in
general, a diminished pressure existing at some particular region
is the cause rather than the effect of the rapid whirling motion :
though in some respects indeed these two conditions can be re-
garded as being mutually causes and effects, each being essential
to the maintenance of the other, while there are also some further
promoting causes or conditions not as yet here mentioned.

It seems indubitably to be the truth that ordinarily for the
genesis of a whirlwind the two chief promoting conditions are :
firstly, a region of diminished barometric pressure, this diminution
of pressure being, it may be presumed, due to rarefaction of the
atmosphere over that region by heat, and sometimes, further, by
its condition as to included watery vapour; and, secondly, a
previously existing revolutional motion, or differential horizontal
motion, of the surrounding air, such revolutional or differential
motion being not necessarily of high velocity at any part.

The supposed accumulation of air rarefied by heat or other-
wise, for producing the abatement of pressure may, the author
supposes, in some cases extend upwards throughout the whole
depth of the atmosphere ; and in some cases may be in the form
of a lower warm lamina which somehow may have been over-
flowed or covered by colder air above, through which, or into
which, it will tend to ascend : or the lower lamina may in some
cases be warmed in any of several ways, and so may get a tend-
ency to rise up through the colder superincumbent atmosphere.

150 PAPERS RELATING TO MOTION OF FLUIDS [27

On this part of the subject the author believes there is much
scope for further researches and advancements both observational
and considerational ; — that is to say, by encouragement of a spirit
towards accurate observation; and by collection and scrutiny of
observed facts and appearances ; and by careful theoretical con-
sideration founded on observational results or suppositions.

To the author it seems probable that the great cyclones may
have their region of rarefied air extending up quite to the top of
the atmosphere ; while often whirlwinds of smaller kinds, many
of the little dust whirlwinds, for instance, which are frequently
to be seen, may terminate, or gradually die out, at top in a layer
or bed of the atmosphere different in its conditions, both as to
temperature and as to original motion, from the lower layer in
which the whirlwind has been generated. In many such cases
the upper air may probably be cooler than the lower air in which
the whirlwind originates.

On the subject of the actions going on at the upper parts or
upper ends of whirlwind cores, in most cases, the author feels that
he is able to offer at present little more than suggestions and
speculative conjectures. In very many descriptions of the appear-
ances presented by those whirlwinds with visible revolving cores,
which are called waterspouts, it is told that the first appearance
of the so-called waterspout consists in the rapid shooting down
from a dense cloud of a black cloudy streak, seemingly tortuously
revolving and swaying more or less sidewise. This is said rapidly
to prolong itself downwards till it meets the surface of the sea ;
and the water of the sea is often imagined and described as
rising up bodily, or as being drawn up, into the partial vacuum
or central columnar place of diminished pressure. The frequently
entertained notion — a notion which has even made its way into
writings by men of science and of authority in meteorology — that
the water of the sea is sucked up as a continuous liquid column
in the centre of waterspout whirlwinds, is by some writers and
thinkers repudiated as being only a popular fallacy, and it is
affirmed that it is only the spray from the broken waves that is
carried up. In this denial of the supposition of the water being
sucked up as a continuous liquid column, the author entirely
agrees, and he agrees in the opinion that spray or spindrift from
the sea, set into violent commotion by the whirlwind, is carried up
in a central ascending columnar core of air.

1884] WHIRLWINDS AND WATERSPOUTS 151

On the other hand, the commonly-alleged inception of the
visible waterspout phenomena, in a descending, tortuously-
revolving, and laterally-bending or swaying cloudy spindle
protruding from a cloud, the author supposes to be so well
accredited by numerous testimonies that it must be seriously
taken into account in the development of any true theory and
explanation of the physical conditions and actions involved. He
ventures to hazard a suggestion at present — perhaps a very crude
and rash one. It is that the rising central core may perhaps, in
virtue of its whirling motion and centrifugal tendency, afford
admission for the cloudy stratum to penetrate down as an inner
core within that revolving ascending core now itself become
tubular. The cloudy stratum may be supposed not originally to
have been endowed with the revolutional motion or differential
horizontal motion with which the lower stratum of thermally
expanded air has been assumed to be originally endowed. The
upper stratum of air from which the cloudy spindle core is here
taken to protrude down into the tubular funnel is not to be
supposed to be cold enough to tend to sink by mere gravity.
Though it were warm enough to allow of its floating freely on
the thermally expanded air below, it could still be sucked down
into the centre of the revolving ascending core of the whirlwind.

Not to proceed further on this occasion with attempts towards
explanation of the difficult subject of the actions at the upper
ends of waterspout whirlwinds, the author wishes to have it
understood that his main object in proceeding to prepare the
present paper was to put forward clearly the theory he has given
as to influx at the bottom in consequence of abatement of whirl
in the lamina close to the sea-surface by frictional resistance
there.

Addendum. — A few brief explanations and references will
now be added to assist in the understanding of some of the
principles assumed in what has been already said. It is to be
clearly understood that, in a whirling fluid, even if the velocity
of the whirling motion be very small at great distances from the
axis, if the fluid be impelled inwards by forces directed towards
the axis, the absolute velocity will greatly increase with diminu-
tion of distance from the axis. Thus in the whirlpool of free
mobility, in which the particles are perfectly free to move out-
ward or inward, the velocities of the particles are inversely

152 PAPERS RELATING TO MOTION OF FLUIDS [27

proportional to the distances from the axis, the fluid being
understood to be in viscid or frictionless. On this subject reference
may be made to a paper by the author on "Whirling Fluids,"
published in the British Association volume for the Belfast
Meeting, 1852*. Again, as to the inward flow caused in a fric-
tionally retarded bottom lamina of a whirlwind or whirlpool
with vertical axis, by the frictional retardation from the bottom
on which the whirling fluid rests, reference may be made to a
paper by the author, "On the Grand Currents of Atmospheric
Circulation" in the British Association Report, Dublin Meeting,
1857, Part II. p. 38f. On another case of the manifestation of the
same principle, reference may be made to a paper by the author
in the Proceedings of the Royal Society for May 1876J, in respect
to the "Flow of Water round Bends in Rivers, &c.," with reference
to the effects of frictional resistance from the channel in the
bends; and to another paper by him, on the same subject, in
the Proceedings of the Institution of Mechanical Engineers
(August 1879, p. 456 §), where the inward flow is explained as
experimentally exhibited.

Postscript of date August 16. — Prof. James Thomson wishes
now to offer in continuation of his paper on "Whirlwinds and
Waterspouts," despatched two days ago for Montreal the following
postscript, which will extend the considerations there already
put forward, and will tend to modify or amend some of them ;
but will leave unchanged the theory as to influx of the bottom
lamina of the whirlwind towards the central region in consequence
of the frictional resistance offered by the surface of the sea to the
air whirling in close contiguity upon that surface.

He wishes to put forw:ard the question as to whether it may
not be possible, in some cases of whirlwinds, for the barometric
pressure in the central or axial region to become abated through
the combined influences of rarefaction by heat (increased, perhaps,
by conditions as to included moisture) on the one hand, and the
whirling motion on the other hand, very much beyond the abate-
ment that could be due to heat, or heat and moisture, alone,
without the whirling motion. He thinks it very likely that in
great whirlwinds, including those which produce the remarkable
phenomena called waterspouts, it may be impossible for the

* [No. 1, supra, p. 1.] t [No. 20, supra, p. 144.] $ [No. 16, supra, p. 96.]
§ [No. 18, supra, p. 102.]

1884] WHIRLWINDS AND WATERSPOUTS 153

whirling action to be confined to the lower region of the atmo-
sphere; but that, even if commenced there, it would speedily
be propagated to the top. It seems also not unlikely, and in
some trains of thought it comes to appear very probable, that the
whirling fluid, ascending by its levity, would drive outwards
from above it all other air endowed with less Avhirling energy, and
would be continually clearing away upwards and outwards the
less energetic axial core which enters from below, and any, if
such there be, that has entered from above. He is unable at
present to offer much in further elucidation (possibly it might
only prove to be in further involvement) of this very difficult
subject. He thinks the question should at least be kept open as
to whether the whirling and scouring action may not go forward
growing more and more intense, promoted always by energies
from the thermal sources which have produced differences of
temperature and moisture in different parts of the atmosphere,
and that thus a much nearer approach to vacuum in the centre
may be caused than would be due merely to the levity of the
superincumbent air if not whirling.

He also wishes to suggest that the dark and often frightful
cloud usually seen in the early stages of whirlwinds and water-
spouts, and the dark columnar revolving core often seen appa-
rently protruding downwards from the cloud, may be due to
precipitation of moisture into the condition of fog or cloud, on
account of abatement of pressure by ascension in level, and
environment with whirling air, which by its centrifugal tendency
acts in protecting the axial region from the pressure inwards of
the surrounding atmosphere.

28. BAKERIAN LECTURE. — ON THE GRAND CURRENTS OF
ATMOSPHERIC CIRCULATION.

[From the Philosophical Transactions of the Royal Society. Received
March 10, Read March 10, 1892.]

[Professor Thomson died on May 8, 1892, before this Lecture was printed.]

IN the early times of the Royal Society (a little more than
200 years ago) a spirit of inquiry and of speculation as to the
causes of the Trade Winds arose among its members. The papers
which we may presume to have first brought the subject into

154 PAPERS RELATING TO MOTION OF FLUIDS [28

special notice in the Society, and which were published in the
Transactions, offered views which, in the light of subsequent
knowledge and theory, show themselves as being untenable, and
in part even grotesque. But those papers were soon followed by,
and probably had an effect in leading to, a much more important
paper by the eminent astronomer Edmund Halley ; and this was
followed 49 years later by one, more important still, by George
Hadley, in which we may with confidence judge that a substantially
true theory of a large part of the system of Atmospheric Circulation
in its grandest and most dominant conditions was for the first
time offered to the world through the pages of the Philosophical
Transactions.

Further speculations on the subject and advances in our
knowledge of it have been made in later times and have been
brought into notice in various ways. I believe that I have
myself arrived at some improved considerations which are to a
large extent trustworthy and go far towards completing the true
theory of the grand currents of atmospheric circulation, and
I entertain the ambition to have my views placed on record by
this Society — the Society in which the subject had its most
important beginnings.

With this in view it appears indispensable that some historical
recital should be adduced of the progress made by others previously:
but still, for those who may at any time wish to direct their
attention specially to the physical conditions irrespective of the
history of the progress of thought or of discovery on the subject,
it appears desirable that an exposition of the resultant theory
which I have devised should be presented without being itself
encumbered by historical details of the courses through which it
has been ultimately arrived at. I propose, therefore, to present,
in a first section, a historical sketch of all the speculations and
theories which, as far as known to me, have conduced in any
important way towards the resulting theory that I have to offer
as being tenable and trustworthy ; and then to set forth that new
theory itself divested as far as possible of historical or personal
references ; and to conclude with some considerations as to the
reasons for or against the views put forward by various persons.

The first opening up of considerations and discussions in the
Royal Society on the subject of Atmospheric Circulation appears
to have been made in a paper submitted to the Society, in 1684,

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 155

by Dr Martin Lister, Doctor of Physic of the University of
Oxford, and published in the Transactions*. As an illustration
of the scanty and crude condition of knowledge and of thought
on this great subject at that time — the middle period of the
life of Sir Isaac Newton — I may be permitted to cite the
views of Dr Lister in his own words as offered briefly in that-
paper : —

"Among the known Sea Plants, the Sargosse, or Lenticula
Marina, is not to be forgot; this grows in vast quantities from
36 to 18 Degrees Northern Latitude, and elsewhere, upon the
deepest Seas. And I think (to say something by the by of that
great Phenomenon of the Winds) from the daily and constant
breath of that Plant, the Trade or Tropick Winds do in great
part arise : because the matter of that Wind, coming (as we
suppose) from the breath of only one Plant it must needs make it
constant and uniform : Whereas the great variety of Plants and
Trees at Land must needs furnish a confused matter of Winds :
Again the Levant Breezes^ are briskest about Noon, the Sttn
quickening the Plant most then, causing it to breathe faster, and
more vigorously ; and that Plants mostly languish in the night is
evident from many of them which contract themselves and close
at that time; also from the effects of our winters upon them,
which cause them to cast both fruit and leaves too ; whereas they
are said (the same Plants for kind) universally to flourish all the
year alike within the Tropicks.

"As for the direction of this Breeze from East to West, it may
be owing to the General current of the Sea, for a gentle Air will
still be led with the stream of our Rivers, for example. Again
every Plant is in some measure an Heliotrope, and bends itself,
and moves after the Sun, and consequently emits its \apours
thitherward, and so its direction is in that respect also owing in
some measure to the Course of the Sun."

(NOTE. — The above is the whole passage given by Dr Lister
about Trade Winds. The rest of his paper relates to entirely
different subjects, chiefly to salt springs and brines.)

In scrutinizing these utterances of Dr Lister, we may notice
that he must have been in possession of some information, more

* Phil. Trans. No. 156, p. 494. Date February, 1683-84.

f By "Levant Breezes" here Dr Lister obviously means breezes from the east,
in fact, the Trade Winds of the tropics. — JAMES THOMSON.

156 PAPERS RELATING TO MOTION OF FLUIDS [28

or less vague, to the effect that over extensive regions of the
great oceans between the Tropics, or near to them, winds blowing
from east towards west are prevalent ; and that he has attempted
to explain this prevalence by attributing it to the breath of a
plant floating on the sea and turning "as an heliotrope" so as to
blow its breath westward according to the direction of the Sun's
diurnal relative motion through the sky from its rising in the
east to its setting in the west. He does not indicate any
knowledge of the fact that on the two sides of the Equator in
tropical regions there are two Trade-Wind zones; one on each
side, in each of which the wind prevails from east to west, with
an accompanying motion in each case towards the Equator.

We may, indeed, suppose that such knowledge was only
gradually acquired, chiefly by mariners, and was but vaguely
and imperfectly intercommunicated among them, and was spread
very little among others during a long period of time. I do not
suppose that any remarkable step in the discovery and promul-
gation of knowledge of the prevalent courses of the winds in
those seas in and about the Torrid Zone is to be attributed to
any one person in particular, nor that there was, indeed, any
very important and clear promulgation of the floating knowledge
on the subject until the time when the astronomer, Halley,
collected and systematized a large amount of valuable information,
and presented it to the Royal Society, in his paper in the Trans-
actions of 1686, to which I shall make particular reference a little
further on.

It may be well at the present stage, before going further into
the history of speculations, to draw attention to the chief features
of the Trade Winds and other perennially prevalent air currents,
as they present themselves very manifestly to the notice of
mariners.

The mariners on board a ship at sea, it is to be observed,
however, have direct cognizance only of the wind blowing at the
spot on the ocean's expanse where for the time being their ship
is situated. They can make no observations on the winds blowing
at the same moment 100 miles away, and the vault of the sky
above them presents to their eyes no adequate indication of the
upper currents, or of the places whence these come or whither
they are going in their circuits. But even long ago, by the
collation among navigators of facts contemporaneously observed

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 157

by various seamen, important knowledge was acquired gradually
as to the general character of contemporaneously existing air
currents at the surface of the sea, without the aid of any trust-
worthy theory as to the continuations of such currents in circulation
through the upper regions of the atmosphere. It is further to
be noticed that the geographical distribution of sea and land,
presenting as it does great regions of ocean, and large continents
themselves varied with mountain ranges and low-lying plains,
introduces great local variations in the conditions determining
the courses of winds, and prevents the institution of any
complete uniformity in the character of the air currents all
round the Equator, or throughout zones between any parallels of
latitude.

But in the Atlantic and Pacific Oceans there are extensive
regions within, and adjacent to, the Torrid Zone, in which the
winds blow with remarkable constancy from the east while con-
verging also from north and south at the two sides, towards a
medial belt of calms and rains which is situated along, or very
near to, the Equator.

These remarkably persistent winds blowing in the northern
hemisphere from the north-east, and in the southern from the
south-east, are called the Trade Winds. The outer limits of the
two Trade Winds vary in different seasons of the year, arid are
affected by casually varying conditions of the atmosphere in other-
parts of the world, and by the geographical configurations of the
surrounding continents affecting them unequally in different
parts; but, without minute exactitude, they may be regarded
as occupying some such breadth as perhaps 25° or 30° on each
side of the Equator.

It was also found by mariners in those early times previous
to the development of theories of atmospheric circulation, that in
the great oceans, in the higher latitudes, outside of the trade-
wind bands, west winds are prevalent in frequency and strength
over winds in other directions. It became the practice of traders
when going on a voyage from east to west to make their way
into the trade- wind region, where they were sure of finding favour-
ing breezes, and on their return voyage to get into higher latitudes,
so as to take advantage of the prevailing west winds there.

Until recent years no information was definitely gathered
from observations or otherwise as to whether or not there be any

158

PAPERS RELATING TO MOTION OF FLUIDS

[28

prevalent general average tendency in those west winds to blow
in their variations more towards the Pole or towards the Equator;
and I avoid entering on any statements on the subject at the
present historical stage, as that matter will be better associated
with the subsequent progress of theories than with the early
history.

The explanations just given in words as to the chief features
of the trade winds and of the wesb winds of higher latitudes may
be supplemented so as to come more vividly before the imagination
by aid of fig.. 1.

This figure is sketched without regard to the disturbing
influences of continents and mountain ranges. It may be regarded
as being suggestive of the most remarkable features which would
probably present themselves in the winds if the surface of the
world were all ocean, or were ocean mottled very uniformly with
small islands.

Now, to revert to the historical sketch already entered on, of
speculations and theories as to perennially prevalent winds, and
to variable winds which manifest perennial prevalence in special
directions, the next theory to which I have to refer, is that of
Dr Garden of Aberdeen, which, about one year after that of
Dr Lister, was placed on record in the Transactions of the Royal
Society. Dr Garden, in his paper*, attributes the east to west

* Phil. Trans. Vol. 15, No. 175. September and October, 1685.

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 159

motion of the Trade Winds of the Atlantic and Pacific Oceans
to the supposed vortices of a supposed ether, or all-pervading
atmosphere, which, according to the planetary system proposed
by Des Cartes, and at that period still believed in by some, were
imagined to be the agents carrying on or sustaining the revolutions
of the Planets round the Sun, and of the Moon round the Earth,
and of the Earth round its own axis. Dr Garden's paper gives
indication of his having some knowledge, not only of prevalence
of winds from the east within the tropics, but also of prevalence
of winds from the west in higher latitudes outside -of the tropical
regions. He gives no indication of knowledge of the Trade Winds
having, along with their westward motion, also motions towards
the Equator from both sides ; and is, in this respect, apparently
on an equality with Dr Lister. They had both made praise-
worthy exertions in collecting and bringing into notice important
results from the observations of mariners and other travellers.
When, however, Dr Garden offers explanations of his supposed
reasons for the blowing from east to west within the Tropics, and
from west to east in latitudes higher than those of the tropical
regions, his statements, in their meaninglessness, quite transcend
the inadequacy of the explanations in the amusing attempt of
Dr Lister.

The papers of these two men may probably have had a
beneficial effect in instigating Halley to prepare, for the Royal
Society, a paper presenting the results of his researches as to the
observable facts of the winds, and his speculations to account for
the prevalent directions of their motions. In 1686, about one
year after Dr Garden's paper, Halley, then at the age of thirty,
submitted to the Society an elaborate and very clear account of
the information as to the winds in different parts of the world
which he could collect from numerous sources, including obser-
vations carefully made by himself on voyages and on land between
the Tropics. The title of his paper in the Transactions, is "An
Historical Account of the Trade Winds, and Monsoons observable
in the Seas between and near the Tropicks, with an attempt to
assign the Physical Causes of the said Winds*." His description
of the observed facts and his theoretical considerations on the
subject, have constituted an important step in the development
of the science of that subject, even though his theory in its most
* Phil. Trans. No. 183, p. 153.

160 PAPERS RELATING TO MOTION OF FLUIDS [28

important part — that which relates to the east to west motion
of the Trade Winds — turns out to be fundamentally untenable.
He adduced, no doubt, in his explanation, an important part of
the real truth as to causes of the wind, a part which, if not first
suggested by him, was clearly either not generally known or not
generally adopted at the time.

This true element in his theory consisted in his assigning as
the primary motive cause of the winds, the expansion of the air
of hot regions, accompanied by its outflow in its upper parts from
those regions towards places of less heat and entailing a diminished
pressure at the base of the ascending heated current, and Conse-
quently entailing an influx at bottom from the lower part of the
atmosphere at the colder places where descending currents are
generated. In applying this general principle further to the
explanation of the observed winds, he rightly explained the influx
of the air from both sides towards the Equator or some medial
part of the trade-wind region as being due to the more intense
heating effects of the Sun in the Equatorial regions. But in the
more important, because less obvious, element for explanation of
the Trade Winds and of atmospheric circulation generally — that
which is requisite for explaining the east to west motions of the
Trade Winds, and the prevalence of winds from west to east in
higher latitudes — he quite missed the true explanation-. He
attributed the east to west flow of the Trade Winds to the
diurnal revolution round the equatorial zone from east to west
of the maximum of accumulation of heating effect from the daily
sunshine, which gives an accumulation of heat in the afternoon
in each successive locality. Briefly, he said to the effect that as
the maximum of accumulated heat runs round the Torrid Zone
from east to west, passing each place at a few hours after noon
of that place, and as the maximum of heat in travelling round
always causes an indraught towards itself, so the atmosphere of
the Torrid Zone must be brought into flowing round from east to
west likewise. But this conclusion from the submitted premises
is really quite inconsequential.

In reference to this speculation, and treating for the present
the direction which we will call the forward direction round the
Torrid Zone as being that of the Sun's progress from east to west,
we may entertain considerations such as the following : — That
consequent on the indraught from all sides towards the hot region,

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 161

where the barometric pressure is most reduced, the backward-
tending forces acting on the air in front of the maximum may be
acting as much in respect to time and duration backward on the
air in front of the maximum as do the for ward- tending forces on
the air behind that maximum, and that, through this consideration
by itself, we might not be entitled to suppose that any resultant
tendency to the generation of a current round the Torrid Zone
one way or other, east to west, or west to east, would be produced.
But when we further consider the unsymmetrical character of
the conditions of the two influxes towards the maximum region
from before and from behind, and the to us very unknown
accompanying frictional conditions between these unsymmetri-
cally conditioned currents of air and the surface of the earth
or sea over which they pass, we may be led to think it very
unlikely that the forwarding and backwarding influences would
exactly counteract one another ; and I certainly think they would
not do so, and I think some resultant flow from east to west, or
from west to east would be produced, but in which way, east to west
or west to east, it would occur I am quite unprepared to say * .

The theory or speculation in the terms in which it was set
forth by its author makes no reference to the inertial conditions
of the atmosphere concerned in its diurnal revolution along with
the Earth, to which, as a matter of fact, it clings so as to have at
all times and all places almost the same revolutional speed or
angular velocity of diurnal rotation as the Earth has. In fact,
Halley's theory would be equally applicable to the case of the
world being non-rotative and having the Sun, or an equivalent
source of heat, revolving round it from east to west.

But, in view of the very powerfully influencing conditions
subsequently brought to light in the theory of Hadley which will
next be adduced, any such feeble causes as those relied on by
Halley must fall practically into insignificance, the indubitable
cause shown in Hadley's theory being such as to be dominant.

In 1735 George Hadley (brother of the John Hadley who invented
the instrument commonly known as Hadley's Quadrant) submitted

* As a matter of curiosity I think it might be interesting in a time of com
parative leisure for some person to make experiments with a spirit lamp or other
heater kept revolving slowly round in a circular path under a circular tray filled
with water, the path being of a little smaller radius than the tray. The question
being, would or would not the water be set into revolutional motion, and if so
would it revolve in the same direction as the lamp or other source of heat does ?

T. 11

162 PAPERS RELATING TO MOTION OF FLUIDS [28

to the Royal Society the paper of which I have made mention
already as supplying for the first time a substantially true theory
of the primarily dominant conditions of atmospheric circulation*.
The paper is entitled " Concerning the Cause of the General
Trade- Winds," and it is right here to notice that Hadley applied
the name General Trade- Winds, not merely to those winds of
equatorial regions to which the name Trade Winds is ordinarily
restricted, but uses it as including also the west-to-east winds
known to be prevalent in higher latitudes, and used in trade by
mariners for ocean passages from west to east. Thus the scope
of his theory must be understood as being much wider than what
would be conveyed in ordinary nomenclature by the name, Theory
of the Trade- Winds.

In his paper, Hadley commences by adopting, as a part of the
whole truth, the view already in his time currently held by others,
that the Sun's heat, intensely applied and greatly accumulated
in the equatorial regions of the Earth, conjointly with the cooler
temperatures of the regions in higher latitudes, is the main and
primary cause of the Trade Winds and other currents of the
.atmosphere. In this way he supposes that at the Equator or
near to it there is a belt of air ascending because of its high
temperature and consequent rarefaction, and an influx from both
sides towards a zonal region of diminished pressure at its base ;
and that from its upper part currents float away to both sides,
northward and southward, and that these continue in the upper
regions of the atmosphere advancing pole-ward until, by cooling
in the higher latitudes, their substance gradually becoming less
buoyant sinks down gradually and returns towards the equatorial
regions as a lower current along the Earth's surface, thence to
renew the circulation by ascent again in the equatorial region.
While indicating virtually that such atmospheric circulation would
be generated, whether in an irrotative world with a source of
heat revolving round it corresponding to the Sun in its apparent
diurnal revolution, or in a world revolving on its axis as does the
Earth, he shows that in the latter case — the case, namely, of the
revolving Earth — in addition to such circulation as has just been
described, east-to-west and west-to-east motions relative to the
Earth's surface would necessarily come into being for reasons which
may be stated or suggested as follows : —

* Phil Trans. Vol. xxxix. No. 437, for April, May, and June, 1735, p. 58.

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 163

If we consider the air in a nearly calm region at the outer
limits of the trade-wind zone, and regard the air at that place as
being at rest relatively to the Earth's surface, and if we consider
it to be drawn over the surface by indraught towards the Equator
without application to it of any other force than that of the
indraught, except what it may receive by friction from the surface
of the Earth, be that land or ocean, this air in arriving at places
always lower and lower in latitude (and consequently further and
further out from the Earth's axis) is coming to places in succession
each moving eastward quicker than the previous one; and thus the
air is arriving successively at places each going quicker eastward
than the air itself was going when at the previous place ; conse-
quently the air in arriving at each new place must obviously have a
slower motion eastward than the Earth's surface at that place has.

Thus throughout that course the Earth must be rushing
forward under the air eastward quicker than the air goes, and
that is the same as to say that the air must be blowing westward
over the surface of the Earth.

In connection with this part of his theory he brings into
notice that, while the surface of the Earth at the outer edges of
the Trade Winds has much less of absolute velocity eastward in
diurnal revolution round the Earth's axis than the surface at or
near the Equator has, yet the trade-wind air, on arriving at the
foot of the equatorial belt of rising air after its course from those
outer parts in higher latitudes, has become imbued with eastward
velocity little less than that of the equatorial surface of the Earth,
the only deficiency in this eastward velocity from that of the
equatorial surface being what is manifested as wind blowing
westward over the Earth's surface, or having in relation to that
surface a moderate westward velocity. He shows, for an example,
that the eastward velocity of the Earth at either of the tropic
circles is less than that at the Equator by about 87 miles per
hour, but yet that the air which comes from calm regions near
the tropic circles to the equatorial belt has, on its arrival at that
belt, an eastward absolute velocity which is only a few miles per
hour in defect of the velocity of the Earth there, the actual defect
being manifested in the relative velocity with which the wind at
the equatorial parts blows westward over the surface of the land or
sea. He explains that this result is brought about by reason that
the air, during its course from the outer edge of the trade-wind

11— 2

164 PAPERS RELATING TO MOTION OF FLUIDS [28

zone to the foot of the equatorial rising belt, is perpetually
being dragged forward eastward by the quicker-moving land or
sea below it, and so its velocity is kept nearly assimilated to that
of the part of the Earth over which, for the time being, it exists,
and is allowed only to be a little less than that velocity.

Such, then, is Hadley's theory, in so far as it relates to the origin
of the Trade Winds of the equatorial regions on both sides of the
Equator. His theory further extends to explain the cause of the
prevalence of winds from west to east in latitudes higher than
those of the winds of equatorial regions, to which, except in the
nomenclature of Hadley himself, the name Trade Winds ha*s been
usually restricted ; and this part of his theory may be represented
as follows : —

The equatorial surface of the Earth has a velocity of diurnal
revolution from west to east of about 1000 miles per hour. The
air of the land and sea at and near the Equator participates
nearly in the same velocity. The ascending equatorial belt of
heated air retains as it ascends an absolute velocity from west to
east nearly the same as that of the equatorial surface of the
Earth. He supposes, then, in his theory, that the air floating
out from the upper part of the rising belt to north and south
over the equatorial zones of Trade Winds, and thence, still in the
upper parts of the atmosphere, spreading over extensive regions
of land and sea in latitudes higher than those of the Trade
Winds, will, on reaching those regions whose velocities of diurnal
revolution are much slower, be rushing forward from west to east
quicker than do the portions of the Earth's surface over which
it successively arrives in floating poleward ; that greater speed
of eastward motion of the air than of the Earth beneath being,
however (as he indicates with a fair approach to clearness), kept
in moderation by influences from the surface of the land or sea
offering resistance to relative motions of the air above it. Further,
he supposes that this upper air, while moving eastward quicker
than does the Earth below it, gradually loses a great part of its
previously acquired heat, and becomes less buoyant, and conse-
quently descends gradually towards the surface of the Earth, the
supply above being always maintained by fresh arrivals from the
equatorial regions; and he supposes that the descending air
brings from aloft perpetually new supplies of west-to-east motion
relative to the surface, and so maintains winds blowing over the

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 165

surface from west to east. The air then, after its descent from
the sky towards the surface throughout extensive regions, must,
I think, necessarily, under his theory — although he does not
explicitly mention this — be supposed to flow gradually back in
the lower levels of the atmosphere towards the Equator, while
also blowing prevalently from west to east, till it reaches again
the outer border of the trade-wind region, thence to go forward
repeating such a circulation as has just been described.

Hadley concludes his paper with a short passage which, con-
sidered in reference to the crude condition of progressive opinions
prevalent in respect to atmospheric circulation up to the time
of the promulgation of his theory, is to be regarded as suggesting,
though in somewhat vague and not entirely correct expression, a
very notable and important principle.

The passage is as follows :—-" That the N.E. and S.E. Winds
within the Tropicks must be compensated by as much N.W. and
S.W. in other Parts, and generally all Winds from any one
Quarter must be compensated by a contrary wind somewhere or
other; otherwise some Change must be produced in the Motion
of the Earth round its Axis."

The really important idea which it appears to me is suggested
in this passage, is that in respect to the Earth's rotation round
its axis the sum of all the forward turning-force-influences
applied by the winds to the surface of the Earth, land and sea
included, must be equal to the sum of all the backward turning-
force-influences likewise applied to the Earth's surface ; so that
these force influences may be such as conjointly to produce no accel-
eration or retardation in the revolution of the Earth round its axis.

In putting forward this idea he was doubtless assuming as a
principle that we are not to attribute to the thermal influence
of the Sun any effects in altering the rotation of the Earth by
producing winds blowing upon the Earth more effectually on the
whole forward than backward, or the reverse. He did not, nor
probably did anyone else till long after his time, notice the now
known principle that the Sun and Moon can, by their attractions,
apply to fluids on the Earth — to the sea or to the atmosphere —
turning forces* which these fluids must communicate to the solid

* Any system of forces which can be balanced by what under the nomenclature
of Poinsot is called a couple, may be described as a turning-force-influence, and
may now with advantage be called a torque.

166 PAPERS RELATING TO MOTION OF FLUIDS [28

earth, and which must, in very long periods of time, make changes
on the Earth's rotation. Such influences, however, are certainly
so very small comparatively to those Hadley had under con-
sideration as occurring in the action of the equatorial Trade
Winds from the east, and the winds of higher latitudes from the
west, that his not knowing of them is not to be regarded as
derogating from the practical or substantial truth and validity of
his Theory of the Winds in its main features.

In the account I have given of Hadley's theory of the
primarily important perennial features of atmospheric circulation,
I have endeavoured faithfully to give a fair and favourable account
of the truths which he brought to light. I have not held it as a
duty to bring under review every statement or phrase to which
objection might be taken by an adverse critic. There is one
mistake, however, into which Hadley fell, arid which is too
important to be passed over without notice. This error, although
incorporated by himself along with his true explanations in
respect to the causes of the equatorial Trade Winds and of
prevalent westerly winds of higher latitudes is quite separable
from those true explanations; and its elimination does -not make
any breakdown in any essential part of his reasoning as to the
real conditions of the atmospheric motions. His error pertained
not to his suppositions as to the actual motions of the real air,
but to supposed motions and behaviour of air in an ideal case
which he adduced as a simplified illustration intended to be
helpful to the consideration of the more complex conditions of
the real case. The two cases — the ideal and the real — are not
explicitly and distinctively specified by himself, but they are brought
implicitly under consideration in his statements to the following
effect : —

Firstly. — That air having been in an approximately calm
condition at one of the Tropic Circles, and having moved thence
in the Trade Wind to the Equator, will, on arriving at the
Equator, retain still the same absolute eastward velocity that it
had when at the Tropic, and so will at the Equator have less
velocity of absolute eastward motion than the Earth there has,
by 2083 miles per day, or 87 miles per hour, and that so it will
be moving relatively to the Earth there as a wind blowing at the
rate of 2083 miles per day from east to west.

And Secondly: — That as an amendment on the previous

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 167

statement, it is to be considered that "before the air from the
Tropicks can arrive at the Equator, it must have gained some
motion eastward from the surface of the earth or sea, whereby
its relative motion will be diminished, and in several successive
circulations may be supposed to be reduced to the strength it is
found to be of."

In reading these two statements conjointly we may with
confidence judge that the first of them is not meant to convey
the actual truth in respect to the real behaviour of the atmosphere,
but that it is only a theoretical utterance as to an ideal case, in
which the frictional drag between the surface of the ocean and
the atmosphere is left out of account, and that the second is that
which is meant to convey the real truth. Now the important
error into which he has here fallen, consists in his supposing that
in an ideal case, in which the trade-wind air is regarded as
frictionless and free from receiving any eastward or westward
force-influences from the ocean below it, or as I will add, from
the atmosphere immediately above it, it ought to be expected on
arriving at the Equator, from a calm at the tropic circle, to retain
the same amount of eastward absolute motion which it had when
at the tropic. Instead of that, in the ideal case, if fully specified
with due limitations, such as we may suppose were tacitly con-
templated, without being fully thought out, the true averment
would have been that the air on arriving at the Equator would
have a velocity of eastward absolute motion less than that at the
tropic, in ratio inverse of that of the distances of the two places
respectively from the Earth's axis. What I mean here to say,
may, perhaps, without elaborate definitions and specifications, be
tolerably well suggested in brief words, by saying that, in a
vortex of free mobility, with circular motions round an axis, the
velocities at different distances from the axis must be inversely as
those distances.

But now, in truth, the ideal case which Hadley touched upon,
was quite outside of the scope of the real conditions of the
atmospheric motions, which he professed to explain better than
had been done in the attempts of others before his time. He had
amply sufficient reason for his averment, to the effect that the
real trade-wind air in its approach from the tropic to the Equator,
under the influence of indraught towards the Equator, should be
expected at each new place nearer to the Equator than the

168 PAPERS RELATING TO MOTION OF FLUIDS [28

previous one, to have a less velocity of eastward absolute motion
than the surface of the sea has at that new place, and that the
frictional drag eastward applied to the air by the sea surface will
only act towards assimilation of the eastward velocity of the air
to that of the water, while still in principle, as in fact, leaving
the air to go slower eastward than does the water — that is, to
blow as a westward wind relative to the ocean. If what he
professed to do had been to bring into notice a. special variety
of vortex motion, constituting what we may call a vortex of free
mobility in a frictionless fluid, and to offer a dynamic theory of
its motions, and if his theory had included such an error as the
one in question ; then his theory would have been fundamentally
erroneous. But such was not at all what he professed to do. He
proposed to explain certain large and very remarkable phenomena
of the observed winds. This he did well, and in doing so he made
a very important advance in development of true theory in respect
to atmospheric motions.

I have touched in some detail on these matters, because
I think that remarks making inadequate recognition of the
importance of Hadley's true discoveries have sometimes been
put forward in our own times.

During a period of more than a century from the time of the
promulgation of Hadley's theory, in 1735, there was, I consider,
little if any remarkable progress made in development of new
speculations for better or for worse in respect to the grand or
perennial currents of atmospheric circulation. A long time
elapsed, in which there seems to have been little or no vigorous
spirit of investigation into the significances or the relative merits
of the speculations which had been propounded, or of effort to
amend the existing theories, or to discover new truths on the
subject. In confirmation of this it may be noticed that we find
that 58 years after the publication of Hadley's paper, Dalton
arrived independently at substantially the same theory as that
part of Hadley's which dealt with the equatorial Trade Winds,
and in his book entitled Meteorological Observations and Essays*,
which in 1793 he was preparing for publication, he gave an
account of his theory, supposing it to be original, but he

*

* Meteorological Observations and Essays, by John Dalton, D.C.L.,F.R.S., 1793.
Of this work there is also a second edition, which is a verbatim reprint issued by
Dr Dalton himself, in 1834.

1892] GRAND CURRENTS OP ATMOSPHERIC CIRCULATION 169

discovered, before the book was issued to the public, that he had
been completely anticipated by Hadley's paper, of the existence
of which he had not been previously aware. In his preface to
that book, after making recognition of Hadley's priority, he goes
on to say : — <; I cannot help observing here, that the following
fact appears to be one of the most remarkable that the history
of the progress of natural philosophy could furnish. — Dr Halley
published in the Philosophical Transactions a theory of the trade-
winds which was quite inadequate and immechanical, as will be
shown, and yet the same has been almost universally adopted ;
at least I could name several modern productions of great repute
in which it is found and do not know of one that contains any
other."..." On the other hand G. Hadley, Esq., published in a
subsequent volume of the said Transactions a rational and satis-
factory explanation of the trade-winds, but where else shall we
find it?"

It is right here to remark further that Dalton in his own
speculations did not touch at all upon the prevalence of west
winds in extra- tropical regions, either as to its explanation or even
as to its existence : and that he does not seem to have noticed or
appreciated the great importance of Hadley's theory in this respect.

Not only before, but also after this episode of Dalton's specu-
lations and researches so published, the theory of Hadley must
certainly have remained but little read in its author's original
paper.

Within the first half of the present century writings on the
winds, including the Trade Winds and general circulation of the
atmosphere, have been very numerous, some of these have
appeared in our encyclopaedias, and others in works on meteorology
and navigation, and have been widely diffused in atlases containing
maps and charts on physical geography.

In such ways many sketches have been presented to the
public as explanations of the Trade Winds and other currents
of the atmosphere related to them, embodying more or less of
the fundamental principles of Hadley's theory, but often without
reference to his name, and usually without due appreciation of
the meaning and importance of his theory. In many of these
cases we may suppose that the authors had never seen his own
original paper, but had obtained their information indirectly
through the writings of others.

170 PAPERS RELATING TO MOTION OF FLUIDS [28

On the other hand, within the period just mentioned — the
first half of the present century — real progress was made in many
ways, in the gaining of new knowledge and the making of a few
new discoveries, chiefly in connection with the temporary and
local disturbances of the atmosphere, and in the bringing together
of information of various kinds to help in the elucidation of the
subject of the winds. The influence of moisture in air of any
given temperature and pressure in rendering the fluid more
buoyant was brought effectually into consideration.

The attainment of information from the practical observations
of mariners and travellers, and especially explorers of the polar
regions, and also from meteorological observatories, was making
gradual but important progress. Considerable progress was made
in the collecting and correlating by many persons of observational
results as to winds and weather and barometric pressures in various
latitudes, and in the presenting for practical use among navigators
and others of the generalized conclusions so derived.

In that course of progressive labours there were included
various speculations or theories as to great storms, commonly
designated as hurricanes, tornadoes, or cyclones. In beginning
to touch on this subject I have to mention that from among
the many persons who may have taken part in researches and
speculations regarding cyclones, those whom I deem the most
noteworthy are Capper, Dove, Redfield, Thorn, Reid, and
Piddington.

Now, within the period which we have at present under
consideration — the first half of the present century — by a very
gradual course of experience, chiefly maritime, and of speculation
based on such experience, it came to be promulgated that violent
storms w7ere generally great whirlwinds ; and so the old name
tornado, of Portuguese origin, suggestive of turning, and the new
name cyclone, used in the sense not merely of circular form, but
also of revolving motion, came to be accepted as well suited for
the designation.

Also it was found that in the centre of a cyclone there is a
region of comparative calm, and that the centre does not remain
stationary, but travels at some moderate speed, taking generally a
curved course over the surface of sea or land.

The discovery also was established beyond room for doubt
that cyclones in the northern hemisphere revolve in the direction

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 171

opposite to that of the hands of a watch situated in their locality
with its face up ; while in the southern hemisphere they revolve
in the same direction as do the hands of a watch situated in their
locality with its face up.

Also it was discovered and promulgated that in the central
region of a cyclone the barometric pressure is remarkably
diminished as compared with that of the general surrounding
atmosphere, and that this condition must necessarily subsist as a
concomitant of the centrifugal tendency or "centrifugal force" of
the revolving air, but whether the diminished pressure was to be
regarded as a result of the centrifugal force of the revolving air,
or as one of the primary causes of the institution of the cyclonic
revolution, seems commonly to have been left unnoticed or to have
been adverted to under erroneously imperfect views.

Dove, for instance, when discussing the tremendously violent
whirling motion which is met with in the inner part of a cyclone
immediately around the central region of remarkable calm, says,
"the diminution of barometrical pressure is not the cause of the
violent disturbance of the air, but rather a secondary effect of it*"
and through that passage with its context it seems doubtless that,
while entertaining the view that the rapid revolving motion of
the air somehow instituted maintains by centrifugal tendency the
diminished pressure in the central region, he fails to notice the
more complete truth, that without the actual occurrence of centri-
petal motion caused by predominating influence of inward suction
the rapid revolving motion would not institute itself at all.

This being said, however, there is yet, of the whole truth,
another element which must be brought into notice, and which
I here briefly describe, with some perhaps new ideas that have
occurred to myself.

It is, that while for a beginning an accumulation of buoyant
air at bottom elongates itself upwards into a shape approaching
to a columnar form, and so effects an abatement of pressure at its
base ; and this abatement of pressure (or suction) induces a
centripetal flow towards that place from outer regions where some
slight, though it may be almost imperceptible, motions having
revolutional momentum (or, in other words, moment of momentum)
round that place may already exist, and the revolving mass of air
through the action of the centreward forces applied to it, takes

* Dove, Laiv of Storms, English translation by Robert H. Scott, M.A., p. 198.

172 PAPERS RELATING TO MOTION OF FLUIDS [28

an increasingly rapid revolving motion; and further, this rapid
motion reacts on the buoyant central column, keeping that from
scattering through the air around it, and so institutes a very lofty
continuous column of the buoyant air.

To make this clearer we may notice that if a buoyant central
column were for a moment existing surrounded by non-rotative
air having greater pressure in its lower parts than that in the
column at the same level, that column could not continue its
existence. The outer air with its greater pressure would press in
on the column, and would increase the pressure in its substance
instantly, but the weight of the upper portion of the buoyant
column would be inadequate to resist the upward thrust so
produced in the lower part, and so the lower parts would shoot
those above them upwards with violently accelerating motion.
Through the rushing upwards so generated a breaking up of the
column would supervene, and its substance would scatter itself
in rolling masses among the surrounding air ; and the two com-
mingling would ascend gradually, and at the same time the
pressure of the surrounding air would communicate itself to the
region where the base of the column had been.

But now, on the other hand, if the mass of air around the
central buoyant column be whirling, it will keep itself out by the
centrifugal tendency accompanying its own rapid revolution, and
so will not press in upon and break up that central column of air
of diminished pressure, and thus the abatement of pressure at the
foot of the column will be maintained and will become further
intensified.

To Redfield is due much credit for his able and long-sustained
labours in collecting and correlating observed facts as to cyclones
and the smaller kinds of whirlwinds. He gathered and published*
a very interesting collection of accounts of violent columnar whirl-
winds which formed themselves over large fires of circular masses
of brushwood, the flame and smoke in each case ascending as a
lofty rotating column ; and this has had part in suggesting to me
some elements in the theoretical considerations here briefly
sketched out. In his remarks on these whirlwinds he emphatically

* "Some account of Violent Columnar Whirlwinds which appear to have
resulted from the action of large Circular Fires," by W. C. Redfield. Read before
the Connecticut Academy, of Arts and Sciences, Jan. 22, 1839. Printed in the
American Journal of Science and Arts (Silliman's), 1839, Vol. xxxvi. p. 50.

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 173

brought into contrast the distinction between the flames and
smoke ascending without whirling motion from hot furnaces and
various ordinary fires, on the one hand, and, on the other hand,
the revolving columns of flame and smoke often met with in
those great fires of brushwood in the open air. By his various
researches into the actions and effects of great storms, Redfield
contributed more, perhaps, than any other man to the advance-
ment of observationally-derived knowledge of their cyclonic
character and features.

Wild and fantastic notions were, however, afloat in those times
as to the origin of cyclones. Thus Piddington, in his well-known
work entitled the Sailor s Hornbook, even in the edition so late
as I860*, in stating his resultant opinions and conclusions, makes
such statements as the following : —

That he considers cyclones to be flat circular disks which may
be formed at the sides and upper and lower surfaces of clouds,
and which, once formed, may either rise higher or descend down-
wards, and may extend themselves greatly or contract in diameter,
and which may be " parallel to the surface of the globe " or
"inclined forwards"; he goes on to say: "It appears to me that
a simple flattened spiral stream of electric fluid generated above
in a broad disk, and descending to the surface of the Earth,
may amply, and simply, account for the commencement of a
Cyclone f."

After making careful search through numerous writings on
the subject of cyclones, I have to say that I have no reason to
think that the investigators who took part in the discovery of the
directions of turning of cyclones in the northern and southern
hemispheres had generally, or that any of them in particular had,
any clear dynamic theory explanatory of the connection between
these modes of turning and the rotation of the Earth, nor even
of the origin of the very rapid whirling motion itself, but I have
found strong indications of deficiency of such knowledge. Even
Herschel, so late as 1857, in his article on "Meteorology," in the
Encyclopaedia Britannica^, stated that a complete account of the
phenomena of cyclones had been afforded "by Hadley's theory as
developed by Dove in his Law of Rotation, and applied to this

* Sailor's Hornbook, third edition.

f Sailor's Hornbook, third edition, p. 338, section 410.

J Encyc. Brit, eighth edition, Vol. xiv. p. 650.

174 PAPERS RELATING TO MOTION OF FLUIDS [28

specific class of aerial movements by Professor Taylor," and then
went on to give what we may presume to be that explanation,
but the explanation he gives, although containing enough of
truth to prove the connection between the direction of the
Earth's rotation and that of the mode of turning of cyclones in
each hemisphere, is incomplete, and is vitiated by important
errors of principle.

Mr Wm. Ferrel, of Nashville, Tennessee, in a paper of date
1856 (to be referred to further on in connection with other
matters), adduced dynamic considerations of more advanced
character for explanation of causes of the gyratory motions of
cyclones; but his treatment, although in some respects usefully
suggestive and indicating sufficient reason for the direction of
turning in each hemisphere, I cannot regard as being on the
whole to very good effect.

Also, as a further result of the researches and scrutinies and
efforts towards generalization told of already, it came gradually
into notice and into acceptance as an established truth that in
the latitudes outside the limits of the Trade Winds extending
far towards the poles, sometimes for brevity called the middle
latitudes, the wind, while prevailing from the west as had been
long previously known, prevails also for each hemisphere more
from the Equator towards the Pole than from the Pole towards
the Equator, so that, on the whole, to take for simplicity the case
of the northern hemisphere, the prevalent average atmospheric
current at the surface of the Earth in those latitudes was judged
to be from the south-west ; or, rather, without particularizing one
exact point of the compass, and with allowance for great variations
in different localities, and at different times, we may better say
from south of west towards north of east.

To account for the component from the south in these
westerly winds of our middle latitudes, it came to be supposed,
for instance, by Leopold von Buch* prominently, as also by many
others, that the air departing for the northern hemisphere from
the top of the Equatorial Belt of buoyant air, while flowing

* Leopold von Buch, Gesammelte Schriften, Vol. in. Berlin, 1877, where there is
to be found his " Physikalische Beschreibung der Canarischen Inseln," Berlin, 1825,
chapter 2, " Bemerkung iiber das Klima der Canarischen Inseln," pp. 288, 289, and
290. A slightly abbreviated translation of the passage in question is given in
Dove's Law of Storms, Scott's translation, 1862, p. 39, in a chapter entitled " The
Upper Return Trade Wind."

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 175

northward still in the lofty regions of the atmosphere and over
the trade-wind zone, soon becomes a current from the south-
west, and continues after descending to the Earth's surface at the
northern border of the trade-wind region still to move forward in
continuation of its old course as a current from the south-west.
But why in the lower regions a pole-ward motion should be
maintained rather than a return flow towards the Equator, and
how the return from higher to lower latitudes to compensate for
this supposed pole-ward surface current should be accomplished,
are questions which appear to have been scarcely mooted or to
have been left enshrouded in vagueness.

Many examples might be cited indicating the wide currency
which such conclusions attained to, but one or two may suffice.
Thus, for instance, in Johnston's National Atlas, of date 1843, we
have a map of the winds by Dr Heinrich Berghaus, of Berlin,
on which the zone of south-westerly winds of middle latitudes
is described in mysteriously poetic words more captivating to the
imagination than satisfying to the reason, as ''Region of South-
westerly Currents of Air, or of the downward returning North-
Eastern Trade Wind in Triumphal Conflict with the Northern
Polar Currents."

Herschel, in his Astronomy*, of date 1850, gives an account
for explanation of the south-west winds of middle latitudes
substantially to the same effect as that of Leopold von Buch and
Berghaus, and with like vagueness as to the return currents from
higher towards lower latitudes.

But from the shelter of that prevalent vagueness, Maury, in
1855, stepped out and boldly offered a scheme of the general
currents of atmospheric circulation which he supposed to prevail,
in courses extending from Pole to Pole, and traversing in different
ways the lower regions of the atmosphere next the surface of the
Earth, and the upper regions which present themselves less
directly to the observation of men. Fig. 2 is a copy of his
diagram which, in conjunction with his printed explanations, sets
forth his scheme of supposed circulation f.

That figure shows a hemisphere of the Earth's surface taken

* Third edition.

t Maury's Physical Geography of the Sea. The first and second editions
appeared in 1855. The statements here made apply alike to his second and sixth
editions, and presumably also to other editions.

176

PAPERS RELATING TO MOTION OF FLUIDS

[28

from Pole to Pole. The continents and lands generally are not
exhibited, and their disturbing effects on the atmospheric motions
are left almost entirely out of consideration. The circulation
imagined and described by Maury in connection with the diagram
is meant to be a fair representation of what he would suppose
likely to be realised in case of local and temporary disturbances
and irregularities being only in a small degree effective. His

Belt of Equatorial Calms and Mains

MAURY-1855.

Fig. 2.

supposed circulation may be thus described : — He supposes that
the air entering the Belt of Equatorial Calms from the southern
hemisphere rises there to the lofty regions of the atmosphere,
and flows thence as an upper current to the Belt of the Calms
of Cancer where it descends to the bottom, from whence it travels
on as a south-west wind over the surface of the sea to the high

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 177

latitudes round the Pole ; and that then ascending at and near
the Pole, it flows as an upper current out to the Calms of Cancer,
where it sinks again to the bottom of the atmosphere crossing
the current already mentioned as descending there, and then
passes along the surface of the sea as a bottom current forming
the north-east Trade Wind, and then enters the Belt of Equatorial
Calms, rises there, crossing the previously mentioned rising current
there, and thence departs as an upper current towards the Calms
of Capricorn, to go through a circulation in the Southern Hemi-
sphere which is an exact counterpart of that already described
for the Northern Hemisphere. The supposed currents are further
indicated by arrows in the diagram, which, on inspection, may
easily be understood. It is to be understood that the diagram
shows a hemisphere of the surface of the Earth with the two
trade-wind zones exhibited one on each side of the Equator,
and separated by the Equatorial Belt of Calms and Rains, which
is often also called the Doldrum Belt. And that it also shows
the two Border Belts, or Calms of Cancer and Capricorn; and
also, in the Northern Hemisphere, the zonal region of wind
prevailing from south of west, and, in the Southern Hemisphere,
the corresponding zone of prevalent winds from north of west.
The arrows shown on the surface of the globe throughout these
various zones indicate the directions of motion of the bottom
currents of the atmosphere constituting the winds blowing on the
surface of the sea. Around the representation of the globe the
atmosphere is shown in section with arrows to indicate the north
and south, and up and down motions in the circulation, which has
just now been described in words.

In offering this scheme of atmospheric circulation, Maury
himself, in respect to the part of it which he propounds as
taking place in the regions between the trade-wind zones and
the Poles, confesses that it is "for some reason which does not
appear to have been very satisfactorily explained by philosophers "
that the currents he supposes do take place instead of their
contraries. In short, he admits that he does not think reason
has been found why in those regions the lower current should be
towards the Pole and the upper towards the Equator, instead of
what we might more obviously expect — namely, a flow towards
the Pole in the upper regions of the atmosphere, and a return
current towards the Equator in the lower regions close upon

T. 12

178 PAPERS RELATING TO MOTION OF FLUIDS [28

the surface of the sea. He even describes the known prevalent
motion of the bottom layers of the atmosphere towards the Pole
in extra-tropical latitudes as being seemingly paradoxical as to
its reason, and although he offers an argument for abatement of
the paradox, that argument on the slightest consideration may
readily be seen to be futile.

In 1856 — the year following after the publication of Maury's
scheme of circulation in his book entitled The Physical Geography
of the Sea — quite a new theory was put forward by Ferrel in a
paper on "The Winds and the Currents of the Ocean," published

FERREL-1856.

Fig. 3.

in the Nashville Journal of Medicine and Surgery*. The scheme
of circulation which he then proposed and upheld by mathematical
reasonings is illustrated in his paper by a diagram, from which
fig. 3 here is taken as a copy. This scheme, as may be noticed
by reference to the diagram, and as may be further ascertained
by reference to the original paper, includes for each hemisphere

* October and November, 1856. This essay is to be found reprinted in Pro-
fessional Papers of the U.S.A. Signal Service, No. 12, published by authority of the
Secretary of War, Washington, Office of the Chief Signal Officer, 1882.

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 179

three zonal rings of atmosphere, making six in all, each having a
separate circulation for itself, except that some small amount of
commingling would necessarily take place at each narrow annular
interface of meeting between two contiguous zonal rings. For
either hemisphere one of these zonal rings of atmosphere covers
the trade-wind region of that hemisphere, another covers the
middle latitudes in which winds prevail from south of west in the
northern hemisphere, and north of west in the southern, and the
third covers the polar region.

Now, attention for simplicity being confined to the northern
hemisphere, explanations of the scheme may be continued as
follows : —

In the trade-wind zonal ring the bottom current flows from
the Calms of Cancer as the Trade Wind to the Equatorial Belt
and rises there, and flows then in the upper regions of the
atmosphere till it comes to a situation aloft nearly over the Calms
of Cancer, and thence it descends obliquely to the Calms at
bottom to flow again towards the Equator, and so to begin
another circuit alike in character to the one now described. Next
in the zonal ring of the middle latitudes, according to the scheme,
the current of air taken as beginning at the Calms of Cancer
advances in the lower regions over the surface of the sea as a
wind from south of west till it comes to about the Arctic Circle
where it ascends to the upper regions, to begin a return course
proceeding southwards as an upper current till it comes to places
aloft nearly over the Calms of Cancer, thence to descend to those
Calms below, and so to complete its circulation from some part
of that belt back again to the same belt. Next as to the
supposed circulation in the zonal ring of the Arctic Regions, it
may suffice to say briefly that the lower current is asserted to be
from the Pole and the upper current towards the Pole, the ascent
from the lower to the upper being at or near to the Arctic Circle,
and the descent being in a region closely surrounding the Pole,
all as may be seen by inspection of the diagram.

Ferrel, in setting forth in his paper his scheme of circulation
and his theoretical reasonings on the subject, introduces as a
fundamental principle in it the assertion that there must be a
heaping up of the top layers of the atmosphere to a maximum
height at about the parallel of 28° and a "depression" of them
over the Equator, and also a "depression" of them at and around

12—2

180 PAPERS RELATING TO MOTION OF FLUIDS [28

the Poles and in high latitudes generally, and his diagram is
purposely drawn to represent these features.

What has now been said is enough to give a good general
idea of Ferrel's scheme of Atmospheric Circulation of 1856. His
assumptions, his reasonings, and his conclusions are, I may say
with confidence, pervaded by impossibilities and incongruities.
But notwithstanding this his paper is deserving of credit for the
praiseworthy efforts it manifests towards a more complete con-
sideration of important principles bearing on the subject, which
had previously been unknown or neglected or imperfectly touched
upon by others.

While I have told of this paper by Mr Ferrel at the present
stage in order of dates, yet I deem it right to explain here that
I had no knowledge of its existence, nor of any of its author's
views, until some years after the publication of the new theory
by myself, about which I have to tell forthwith in the present
paper.

Through a paper* read before the Natural History and Philo-
sophical Society of Belfast in 1856, by Mr Joseph John Murphy,
of that town, interest was strongly aroused in my mind, in the
question of what ought to be supposed to be the true state of
the case as to the courses of atmospheric circulation in the zonal
regions situated between the trade-wind zone and the Pole in
each hemisphere. In that paper Mr Murphy brought under
notice of the Society the scheme of currents of atmospheric circu-
lation set forth by Maury, as the truth ; and gave a theory or
course of reasoning formed by himself, for explaining on dynamic
principles how those supposed motions should be accounted for.

On the subject so presented for consideration, I had to judge
that Mr Murphy's course of reasoning was not valid for sustaining
Maury's theory of the atmospheric motions, and I had to judge more-
over, that Maury's theory was itself, in so far as it dealt with the
circulation outside of the trade- wind zones, entirely untenable and
impossible.

Mr Murphy's course of reasoning, however, included within it
one important element not limited in its scope to the application
made of it in that particular course of reasoning. It was the
supposition that the low barometric pressure of Polar regions

* On the Circulation of the Atmosphere, by Mr Joseph John Murphy, Belfast
Natural History and Philosophical Society, 27th February, 1856,

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 181

and other high latitudes, already discovered as a fact, through
observations of voyagers and others, was to be regarded as due
to the centrifugal force of the air revolving from west to east
throughout the great cap of atmosphere covering the middle and
high latitudes.

Having rejected Maury's theory, and having got the benefit
of the valuable suggestion just referred to in Mr Murphy's paper,
I succeeded in framing a new theory for the circulation in the
regions outside of the trade-wind zones. That new theory I put
forward in a paper read by me at the meeting of the British
Association, held at Dublin, in the following year, 1857 ; and a
clear account of it is to be found in the Abstract of the paper
published in the British Association volume for that year.

The verbal explanations given in the reading of that paper
before the meeting were illustrated by a drawing showing the
scheme of circulation described in the paper. Fig. 4, here given,
is an accurate copy of that drawing, differing from it only in some
unimportant matters, such as in the number of arrows shown,
and in its being drawn with abatement of some exaggerations
which were made in the original in order to render small features
more readily visible at a distance in a large room. The full
significance of the original in all respects is retained unchanged
in the copy here.

In endeavouring to penetrate the mystery as to what the
courses of circulation might be in the middle and higher latitudes,
I was in preliminary ways fully satisfied that Hadley's theory*
in its main features — those, in fact, which in the present paper
I have already described with commendation — must be sub-
stantially true, and must form the basis of any tenable theory
that could be devised.

Now, under Hadley's theory, when we come to consider what
may be the courses of circulation that we should attribute to the

* Reference having been made in the text here to my paper read at the British
Association Meeting for 1857, on the "Grand Currents of Atmospheric Circulation,"
and to the Abstract of it printed in the volume of the Association for that year,
I have to mention as a correction that the theory here described and correctly
designated as Hadley's Theory, was in the printed Abstract erroneously named as
Halley's Theory. I was led into that mistake as to authorship of the commonly
accepted explanation of the trade winds, through my finding it designated as
" Halley's theory of the trade winds " by Maury, in his Physical Geography of the
Sea, to whose newly proposed views in that book my attention was at the time
specially applied.

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PAPERS RELATING TO MOTION OF FLUIDS

[28

atmosphere in the latitudes outside of the trade-wind zones, we
should naturally be led to expect (as I have pointed out in some
detail in an earlier part of the present paper in describing his
theory) that the great sheet of air floating out from the Equator
in the upper regions of the atmosphere towards either Pole, while
having a motion towards the east also, would gradually cool in

THOMSON-1857.

Fig. 4.

advancing to higher latitudes, and would therefore descend in
middle and high latitudes to the Earth's surface and would next,
as a bottom current, flow back towards the Equator while also
flowing eastward, and so would be a current towards the Equator,
not towards the Pole. But, on the other hand, it had been

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 183

brought out through accumulated observational results that the
winds of middle latitudes while blowing towards the east, which
so far is in agreement with Hadley's theory, do, in opposition to
what would be expected under that theory, blow more towards
the Pole than from the Pole. Thus the facts and theory seemed
to be at variance. It then occurred to me that facts and theory
could be reconciled by supposing that the great circulation brought
into probability under Hadley's theory does actually occur, but
occurs subject to this modification, that a thin stratum of air on
the surface of the Earth in the latitudes higher than about 30° —
a stratum in which the inhabitants of those latitudes have their
existence, and of which the movements constitute the observed
winds of those latitudes — being by friction and impulses on the
surface of the Earth retarded with reference to the rapid whirl
or vortex motion from west to east of the great mass of air above
it, tends to flow towards the Pole, and actually does so flow under
the indrawing influence of the partial void in the central parts of
that vortex, due to the centrifugal force of its revolution. Thus
it appeared to me that in temperate latitudes there are three
currents at different heights : — That the uppermost moves towards
the Pole and is part of a grand primary circulation between
Equatorial and Polar Regions; — that the lowermost moves also
towards the Pole, but is only a thin stratum forming part of a
secondary circulation ; — that the middle current moves from the
Pole and constitutes the return current for both the preceding ; —
and that all these three currents have a prevailing motion from
west to east in advance of the Earth. This was the substance
of the new theory which I framed and which, in 1857, I sub-
mitted to the British Association at its Dublin meeting*. The
atmospheric currents supposed under this theory are indicated by
arrows in the diagram, fig. 4, and may be traced out readily on
inspection. This drawing it is to be understood is not intended
to offer any indications of supposed variations in height from
bottom to top of the atmosphere in different latitudes.

I exhibited at the meeting, as an illustration, a simple experi-
ment easily extemporizable on any occasion. It is mentioned in
the printed abstract briefly in the following words: — "If a shallow
circular vessel with flat bottom, be filled to a moderate depth
with water, and if a few small objects, very little heavier than

* [Supra, p. 144.]

184 PAPERS RELATING TO MOTION OF FLUIDS [28

water, and suitable for indicating to the eye the motions of the
water in the bottom, be put in, and if the water be set to revolve
by being stirred round, then, on the process of stirring being
terminated, and the water being left to itself, the small particles
in the bottom will be seen to collect in the centre. They are
evidently carried there by a current determined towards the
centre along the bottom in consequence of the centrifugal force
of the lowest stratum of the water being diminished in reference
to the strata above, through a diminution of velocity of rotation
in the lowest stratum by friction on the bottom. The particles
being heavier than the water, must, in respect of their density,
have more centrifugal force than the water immediately in contact
with them ; and must, therefore, in this respect have a tendency
to fly outwards from the centre, but the flow of water towards
the centre overcomes this tendency and carries them inwards ;
and thus is the flow of water towards the centre in the stratum
in contact with the bottom palpably manifested."

The general hydraulic principle intended thus to be illustrated
by the exhibition of an easily conducted simple case of it is, that
if water were lying, on a revolving flat-bottomed circular plate or
tray, and were revolving at each part quicker than the tray
immediately below that part, a flow would institute itself in the
bottom layer towards the centre, and that this would occur alike
for different speeds of revolution of the tray, and would still take
place, likewise, in the case of the speed of revolution of the tray
being abated to zero. The case of the non-rotative tray was taken
for illustration of the more general proposition simply because of the
facility which that particular case presents for being brought into
visible manifestation, so as to form to an intelligent mind a help to
the imagination in considering the action of the great cap of air
lying on the middle and higher latitudes, and revolving prevalently
at each part quicker than the Earth below that part does. I offer
these explanatory remarks here because in a paper by Mr Ferrel,
to be told of a little further on, my illustration by means of the
non-revolving tray has been made a point of adverse criticism as
to both the nature and the value of the theory I had offered.

Now, before passing quite away from the subject of the
original framing of my own theory, I feel it right to make
special reference to two considerations which were put forward
by Mr Ferrel in his paper of October, 1856.

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 185

Firstly. — Ideas were put forward in that paper by Mr Ferrel
to the effect, that the low barometric pressure found observationally
to exist in polar regions and other high latitudes, is due to the
centrifugal force or tendency of the air of the surrounding middle
latitudes revolving from west to east quicker than does the earth
below: but his views on the matter being unknown to Mr Murphy
and to myself, did not happen to influence my considerations.

And secondly, Mr Ferrel in that paper adduced in connection
with other suppositions an idea which, taking it in a wider scope
than that in which he applied it, and with congruity in application
not pertaining to the case for which he adduced it, I may describe
as implying considerations to the effect that in an atmosphere
covering a zonal region such as that of the middle latitudes, and
having eastward motion relative to the Earth's surface or, what
is the same, having a speed of eastward revolution quicker than
that of the Earth below it, a layer at bottom retarded by friction
on the Earth's surface, and so having less centrifugal tendency than
has the quicker eastward-going air above will be caused to take,
along with its eastward motion, a motion also towards the Pole.

The principle is an important one in its applicability to
atmospheric circulation ; but Mr Ferrel did not apply it to good
account. He applied it only in reference to a system of motions
already assumed by him, but which in the actual atmosphere
are impossible as to causes for their origin and maintenance, and
are incongruous in their mutual relations. His purpose in this
matter was to show reason for the bottom current flowing towards
the Pole while he had the upper current assumed as flowing
towards the Equator. He assumed throughout the whole depth
from bottom to top in his zonal ring of the atmosphere a motion
eastward relative to the Earth, and thereby explained that the
frictionally resisted bottom part should flow towards the Pole.
But now we have to observe that the only reason why under his
theory he can be entitled to assume eastward motion in the lower
portion is because of that portion having been previously assumed
to flow towards the Pole ; and as to the upper portion which he
assumes to flow from the Pole, that reason does not hold at all,
and the upper portion should rather be supposed, under his theory,
to flow westward than eastward. Thus it comes out that he
explained the motion towards the Pole in the lower part of the
atmosphere by first assuming, for no valid reason, a motion towards

186 PAPERS RELATING TO MOTION OF FLUIDS [28

the Pole of that lower part. But now, for the primary assumption
of that motion towards the Pole in the lower portion of the
atmosphere, the reason which he assigned, and which I have just
now treated as being not valid, was his supposed heaping up of
the atmosphere at top, and consequent increased pressure at
bottom at about the parallel of 28° ; but, for the heaping up of
the atmosphere there he needs in the upper region of the atmo-
sphere over the middle latitudes a speed of revolutional motion
greater than that of the Earth's surface immediately below, briefly
a relative eastward motion, so that there may be the necessary
centrifugal tendency for producing the heaping up, and faiat is
incongruous with the flow in those upper regions taking place,
as under his theory he made it do from higher to lower latitudes —
from the Arctic Circle to about the parallel of 28°.

He has not thereby anticipated the new and, I think I may
say, the true theory offered by me, in which the great body of
the lower half of the atmosphere is already shown for good reason
to have motion towards the Equator along with motion from west
to east, but that a comparatively thin lamina at bottom of it, in
virtue of frictional retardation of its eastward motion and consequent
abatement of centrifugal tendency in it as compared to the air above,
is caused to reverse what would otherwise be its motion towards
the Equator, and to take its course towards the Pole instead.

The next publication to which I have to advert is a second
paper by Mr Ferrel. It is entitled "The Motions of Fluids and
Solids, relative to the Earth's Surface ; comprising Applications
to the Winds and the Currents of the Ocean*," and is dated at
its close, "Cambridge, Mass., February, 1860," and is noted on its
title-page as being "Taken from the First and Second Volumes
of the Mathematical Monthly!'

In that paper he offered a scheme of atmospheric circulation
totally different from his previous one of 1856, and entailing a
fundamentally altered theory. In fact, he there abandoned his
arrangement of six zonal vortex rings of circulation, three for the
northern hemisphere and three for the southern, and, instead, he
adopted really the scheme that had been put forward by me

* New York: I vison, Phinney, and Company. London: Triibner and Co., 1860.
It appears that this paper was subsequently republished by the United States
Signal Service in Professional Papers, No. VIII., with extensive notes giving the
mathematical processes in detail by Professor Frank Waldo.

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 187

in 1857 with its two great currents of primary circulation, one
flowing from equatorial to polar regions above, and the other
flowing as a great return current from polar to equatorial regions
below; together with the bottom subordinate current close on
the surface of the Earth in middle latitudes or middle and higher
latitudes, flowing pole- ward on account of the frictional retardation
by the Earth's surface of its eastward relative motion and consequent
diminution of centrifugal tendency.

FERREL-1860.

Fig. 5.

These currents are shown distinctly by arrows in his diagram,
notwithstanding some puzzling confusion introduced by lines
which present the appearance of being meant to indicate average
current lines, but which, in some parts, would suggest impossible
courses, and which show signs of their having been put in without
deliberate care. Fig. 5 here is a copy of that diagram *.

* The same diagram exhibiting his scheme of the winds is repeated in a sub-
sequent paper by Ferrel of date 1861, which he offered as being more popular and
less mathematical. It is to be found reprinted in Professional Papers of the United
States Signal Service, No. XII.

188

PAPERS RELATING TO MOTION OF FLUIDS

[28

The diagram retains two vestiges of his original scheme.
Thus it exhibits distinctly a depression of the top of the atmo-
sphere at the Equator making a place of minimum height for the
atmosphere there; and it retains systems of arrows throughout
the polar regions representing winds having, relatively to the
Earth's surface, motion towards the west together with motion
towards the Equator ; and so in the polar region of the northern
hemisphere representing north-east winds. Both of these features
I regard as having been introduced through mistaken apprehension.
In a later work, indeed, by Mr Ferrel, entitled, A Popular Treatise

FERREL-1889.

Fig. 6.

on the Winds, 1889*, both these features of his former scheme of
circulation are completely eliminated from his scheme and theory
as there presented. This is shown by his diagram f taken in
connection with the printed explanations by which it is accom-
panied. Fig. 6 is a copy of this diagram. The depression of the
top of the atmosphere, or more strictly speaking, the depression

* London: Macmillan and Co.

t Ferrel's Popular Treatise on the Winds, 1889, § 105, p. 155.

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 189

of any isobaric interface in the very lofty regions to a minimum
height over the Equator remains in the diagram, but it is
expressly eliminated by words in the accompanying text. This
diagram, when corrected according to Mr Ferrel's printed words
is, as may readily be seen, essentially the same as my own.

In the closing passage of his second paper, 1860, Ferrel made
mention of the theory given by me at the British Association
meeting in Dublin, 1857, but he did this with erroneous repre-
sentation of the theory, and with inadequate recognition of its
importance and of the fundamental changes he had made from
his own previous theory in adopting the main features of mine
and incorporating them with some remnants of his own previous
views or modes of consideration.

I proceed next to offer some considerations which, I think,
may be of intrinsic interest in themselves, besides helping towards
the development and elucidation of true theory in regard to
atmospheric motions and other conditions.

I have to mention, at this stage, that it may sometimes be
convenient, as an aid towards brevity and clearness in expression,
to characterize air which has no eastward or westward motion
relative to the Earth's surface as having par, or being at par of
revolutional velocity and, likewise, to use the designation over
par of revolutional velocity to signify eastward relative motion,
and under par to signify westward relative motion.

(a) Recalling to notice the theory of Maury and the first
theory of Ferrel given in his 1856 paper, and drawing attention
to the confluence supposed, under both these theories, of two
great upper currents of the atmosphere meeting aloft over the
belt called the Calms of Cancer in the Northern Hemisphere,
and of other two currents likewise meeting over the belt called
the Calms of Capricorn in the Southern, I think it is well to
remark that, if such a confluence were to take place of two
currents, one coming from higher latitudes and the other from
lower to a zonal belt of meeting, the current from the higher
latitudes would have a rapid westward motion relatively to the
Earth below, that is, a revolutional velocity greatly under par,
and the current from lower latitudes would have a rapid relative
motion eastward, or, in other words, a revolutional velocity greatly
over par. They would meet one another obliquely with a velocity
of each relative to the other very great because of its having had

190 PAPERS RELATING TO MOTION OF FLUIDS [28

no frictional mitigating resistance such as the Earth's surface
would afford to currents meeting in like manner at bottom of the
atmosphere. Thus the belt of meeting aloft would be a place of
extraordinary commotion, and this commotion would be propagated
with the two descending currents down to the surface of the
Earth below ; and thus, instead of the Calms of Cancer or
Capricorn we ought to expect to find there a belt of wild and
varying storms. This very simple, and, I think, very obvious
principle, is one of the numerous objections which might singly
or conjointly have checked both Maury and Ferrel in the early
inception of their theories, and might reasonably have prevented
them from propagating views so fallacious.

(b) Next we may raise questions, and proceed to solve them
more or less completely, as to what must be the general character
of the motions of the air at various places in the trade-wind
zone, both in the lower great current approaching to the
Equatorial or Doldrum Belt*, and in the upper great current
departing fro:ji that Equatorial Belt and flowing aloft over the
trade-wind zone to pass over the Border Belt and thence into
what, for want of a better name, we may for the present call the
middle latitudes. In doing this, we shall have to consider and
bring to light some features of the motions of the atmosphere
in the middle latitudes more fully in detail than hitherto in the
present paper.

Let us accompany in thought the progress of a point advancing
with the current along an average stream line, or rather an average
current course in the great under-current from Polar to Equatorial
Regions. For simplicity, let us confine attention to the Northern
Hemisphere. Let us begin the course somewhere within the
middle latitudes. To help imagination we may fix on a point of
commencement situated vertically over New York. The moving
point may, if we please, be idealized as being a small balloon

* This equatorial belt of rising air may also well be called the Medial Belt,
while the Calms of Cancer and Capricorn may be referred to as the Border Belts,
this last especially when it is wished to speak of either of these two indifferently,
without distinction as to whether it be in the northern or southern hemisphere.
Also, either of these border belts may very well be described, or may be named
when desirable, as the Belt of Offturn Parting or briefly as the Offturn Parting.
The reason for this name will be seen readily by inspection of the diagram, where
the great relurn current towards the Equator is parted into two currents, one going
on southwards, and the other turning off towards the north.

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 191

constrained by frictionless guidance to keep in an average current
course while being propelled along that average course by the
more or less varying motions of the surrounding air. Now, during
the progress of the travelling point in its course making way both
eastward and southward, so long as the bottom lamina close to
the surface of the Earth directly beneath the travelling point is
blowing eastward with over-par revolutional velocity, the air above
the bottom lamina there must be going forward with still greater
over-par velocity. The reason for this statement is, that the only
cause for maintenance of eastward relative motion in the friction-
ally restrained bottom lamina is, that the air above in virtue of
revolutional momentum brought from equatorial regions, and not
yet exhausted, is blowing with over-par revolutional velocity, and
driving forward the resisted lamina below. Also, as long as the
over-par velocity is existing in the frictionally resisted bottom
lamina under our travelling point, a flow pole-ward also must
exist in that bottom lamina at the place, for the time being,
directly below the travelling point. This is for reasons fully
explained in the account already given of my own theory. When
further, the travelling point, in making its way southward, arrives
at a stage where that eastward bottom over-par motion no longer
exists directly below, and the travelling point then goes on
making progress further south, it comes to places where the
bottom lamina at the place then below it is moving equator-
ward because of indraught thither, and because all reason for
that lamina's going northward has ceased. Thereafter in the
trade-wind region now entered upon the surface of the Earth
is dragging the bottom air forward revolutionally, and so is
helping it briskly towards the Equator through increasing its
centrifugal tendency.

Then we have to notice that the air, during its course equator-
wards and back again through the trade-wind zone, receives
forward revolutional momentum through the frictional forward
drag applied to it by the Earth's surface, and it loses no revolu-
tional momentum, as the vacuum above the atmosphere can
take none from it. So in departing northwards, as the grand
upper current, it must carry with it far more revolutional
momentum than it had in entering, as the great under current
from the north across the Border Belt; but that great under
current in entering was either at par, or partly at par, and partly

192 PAPERS RELATING TO MOTION OF FLUIDS [28

at over-par, of revolutional velocity; consequently the grand
upper current must depart across the Border Belt with great
over-par of revolutional velocity.

It follows from this, as a corollary, that the top of the atmo-
sphere, or any isobaric interface near the top, must have a
declivity in approaching the Border Belt from the top of the
Equatorial Belt ; and the Border Belt must not have a maximum
height with declivity thence to a minimum at the Equator.

The foregoing demonstration seems also likely to give help
towards the proper interpretation to be put on observational
results recorded by the Krakatoa Committee, and to ^render
highly improbable any suggestions such as seem to be conveyed
in some parts of the report, to the effect that in the very lofty
regions of the atmosphere — at such elevations as 13 miles above
the sea level — a velocity such as 70 miles per hour from east to
west has been indicated in the atmosphere, through the phenomena
manifested after the great Krakatoa eruption.

(c) In connection with the reasoning or demonstration I have-
just given, there is another element which I regard as forming
part of the whole truth, and which must, I think, form an
important element towards the development of the theory more
completely. I have already indicated in the demonstration just
now offered, that the bottom lamina of the atmosphere in the
trade-wind region is especially helped to advance towards the
Equator by the increased absolute centrifugal tendency super-
imposed on it by the forward revolutional drag it there receives
from the Earth's surface; and which communicates to it, through-
out its course towards the Equator, new accessions of revolutional
momentum, and prevents it from getting into under-par of
revolutional velocity, so much as does the air above it in the
great under current towards the Equator. For ready appre-
hension of this, it is well to notice that the under-par and
increased under-par of revolutional velocity imply westward
relative motion in the bottom lamina, and quicker westward
relative motion in the air next above within the great under
current towards the Equator.

This greater abatement of absolute revolutional velocity below
par, or increase of relative velocity westward, constitutes a
condition opposing flow towards the Equator in the main body
of the great under current, and we may reasonably suppose that

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 193

the principal flow towards the Equator takes place in the bottom
lamina — the lamina whose motions constitute the winds notice-
able by action on the sails of ships. So we may suppose that
the main body of that great under current blows nearly due
westward with only a small component of motion equator-ward.
I could not venture, through theoretical considerations alone, to
form an opinion as to the velocity of westward relative motion
which might thus be attained to in the main body of the great
under current, or the velocity of westward relative motion which
might remain in some parts of the upper current proceeding from
the Equator before it has made much advance in latitude to
places importantly nearer the Earth's axis. The complications
involved in the frictional conditions attendant on the flow of
sheets of air with others below and with others above going at
very different velocities render the question practically unsolvable
by theory alone. But I have to point out emphatically that
the Doldrum air, deadened as it is to the condition commonly
spoken of as equatorial calm, is very approximately at par of
revolutional velocity, and when it rises to the top, or to the very
high regions, of the atmosphere, it will have scarcely any west-
ward relative motion, and therefore will not be able to make its
way thence as an upper current pole-ward except by flowing as
we may say down hill, or as we may better say. among isobaric
interfaces down-sloping forward. The lower part of this sheet
of deadened air departing aloft pole-ward, and which lower part
is much below the 'top of the atmosphere, and is in close contiguity
with the current of westward relatively moving air (already just
now mentioned) commencing to move pole-ward without ever having
attained to par of revolutional velocity, will we may suppose, by
buffeting and commingling between it and that westward relatively
moving air, be dragged forward from the Equator, even among
up-sloping isobaric interfaces, in a manner that may be likened
to being dragged up hill.

I might at present extend the explanations and reasonings
on this matter somewhat further, but I abstain from doing so in
order not to prolong unduly the present paper. I prefer to leave
the subject over for further consideration and exposition by myself,
perhaps, and probably by others.

(d) I propose next to offer some considerations in respect to
the atmosphere of the polar regions. For simplicity of expression

T. 13

194 PAPERS RELATING TO MOTION OF FLUIDS [28

I shall speak, in particular, of the polar regions of the Northern
Hemisphere; and I intend that in this, as indeed throughout
nearly all I have said in the present paper, the complications
introduced into atmospheric motions by local distinctions of the
Earth's surface into land and sea are to be, primarily at least,
disregarded.

I consider that we should take as one element of our theories
the principle that we have to suppose a stagnation of impounded
air around the Pole over a great extent of the Polar Regions,
this impounded air being maintained by the influx along the
surface of the Earth of air frictionally deprived of the oVer-par
of revolutional velocity which is possessed by the great cap of
air higher up above the surface of the Earth. This impounded
air lags, I affirm, in the Polar Regions, being unable, for want
of revolutional momentum, and accompanying want of centrifugal
inertial tendency, to take part readily in the great circulation
between polar and equatorial regions. In fact, it cannot get out
from its imprisonment there except by being dragged away through
gradual entanglement with the comparatively rapidly revolving
air arriving by the great upper current from regions having more
rapid revolutional motion and passing away in the great middle
return current towards the Equator.

(e) Further, I may now offer some considerations as to
whether, according to theory, we should expect very clear skies
to prevail in the Polar Region of impounded deadened air.
I think we must suppose the great upper atmospheric current
converging towards the Pole and having over-par of revolutional
velocity must be already very dry, owing to its greatly reduced
pressure and cold temperature. So, when its air descends in
level to return towards the Equator, that air must, I think, be
greatly under its saturation point with water-substance; or, in
other words, must be far from ready to form clouds, or to precipitate
rain or snow. We have to recollect that descending air is generally
very rainless.

On the other hand the bottom flow along the surface of the
land and sea converging towards the Pole I affirm to be moist.
It will be from lower latitudes and generally warmer climates,
and will carry moisture with it from sea and land. This bottom
current will supply water-substance for cloud and snow in the
impounded deadened polar air. The cold of radiation out to

1892] GRAND CURRENTS OF ATMOSPHERIC CIRCULATION 195

interstellar space, coupled with expansion in ascending before it
can join the great middle current of return towards the Equator,
will cause clouds and snow.

I will now conclude this paper by offering a sketch of a
contemplated experimental apparatus for affording practical
illustration of the theory of Atmospheric Circulation which
I have propounded.

The apparatus would consist mainly of a horizontal circular
tray kept revolving round a vertical axis through its centre.
The tray would be filled to some suitable depth with water.
Heat would be applied round its circumference at bottom, and
cold would be applied or cooling would be allowed to proceed in
and around the central part at or near the surface. Under these
circumstances I would expect that motions would institute them-
selves, which would be closely allied to those of the great general
currents supposed under the theory to exist in either hemisphere
of the Earth's atmosphere. The motions of the water, I would
propose, should be rendered perceptible to the eye by dropping
in small particles of aniline dye, and perhaps by other contrivances.
Great variations would be available in respect to the velocity of
rotation given to the tray, and in respect to the depth of water
used, and the intensity of the heating and cooling influences
applied. By various trials with variations in these respects
I think it likely that the phenomena expected could be made
manifest.

13—2

CONGELATION AND LIQUEFACTION

29. THEORETICAL CONSIDERATIONS ON THE EFFECT OF
PRESSURE IN LOWERING THE FREEZING POINT OF WATER.

[From Cambridge and Dublin Mathematical Journal, November 1850 ; taken,
with some slight alterations made by the author, from the Transactions
of the Royal Society of Edinburgh (Jan. 2, 1849), Vol. xvi. Part 5, 1849,
p. 575.

This fundamental paper and the one next succeeding were reprinted in
Sir William Thomson's (Lord Kelvin's) Mathematical and Physical
Papers, Vol. I. pp. 156-164 and 165-169.]

SOME time ago my brother, Professor William Thomson,
pointed out to me a curious conclusion to which he had been led,
by reasoning on principles similar to those developed by Carnot,
with reference to the motive power of heat. It was, that water
at the freezing point may be converted into ice by a process
solely mechanical, and yet without the final expenditure of any
mechanical work. This at first appeared to me to involve an
impossibility, because water expands while freezing; and therefore
it seemed to follow, that if a quantity of it were merely enclosed
in a vessel with a moveable piston and frozen, the motion of the
piston, consequent on the expansion, being resisted by pressure,
mechanical work would be given out without any corresponding
expenditure ; or, in other words, a perpetual source of mechanical
work, commonly called a perpetual motion, would be possible.
After farther consideration, however, the former conclusion ap-
peared to be incontrovertible ; but then, to avoid the absurdity of
supposing that mechanical work could be got out of nothing, it
occurred to me that it is necessary farther to conclude, that the
freezing point becomes lower as the pressure to which the water
is subjected is increased.

The following is the reasoning by which these conclusions are
proved.

First, to prove that water at the freezing point may be
converted into ice by a process solely mechanical, and yet without
the final expenditure of any mechanical work : — Let there be

1849] LOWERING OF THE FREEZING POINT OF WATER 197

supposed to be a cylinder, and a piston fitting water-tight to it,
and capable of moving without friction. Let these be supposed
to be formed of a substance which is a perfect non-conductor of
heat ; also, let the bottom of the cylinder be closed by a plate,
supposed to be a perfect conductor, and to possess no capacity for
heat. Now, to convert a given mass of water into ice without
the expenditure of mechanical work, let this imaginary vessel be
partly filled with air at 0° C.*, and let the bottom of it be placed
in contact with an indefinite mass of water, a lake for instance, at
the same temperature. Now, let the piston be pushed towards
the bottom of the cylinder by pressure from some external reser-
voir of mechanical work, which, for the sake of fixing our ideas,
we may suppose to be the hand of an operator. During this
process the air in the cylinder would tend to become heated on
account of the compression, but it is constrained to remain at 0°
by being in communication with the lake at that temperature.
The change, then, which takes place is, that a certain amount of
work is given from the hand to the air, and a certain amount of
heat is given from the air to the water o*" the lake. In the next
place, let the bottom of the cylinder be placed in contact with the
mass of water at 0°, which is proposed to be converted into ice,
and let the piston be allowed to move back to the position it had
at the commencement of the first process. During this second
process, the temperature of the air would tend to sink on account
of the expansion, but it is constrained to remain constant at 0° by
the air being in communication with the freezing water, which
cannot change its temperature so long as any of it remains
unfrozen. Hence, so far as the air and the hand are concerned,
this process has been exactly the converse of the former one.
Thus the air has expanded through the same distance through
which it was formerly compressed; and since it has been constantly
at the same temperature during both processes, the law of the
variation of its pressure with its volume must have been the same
in both. From this it follows, that the hand has received back
exactly the same amount of mechanical work in the second
process as it gave out in the first. By an analogous reason it is
easily shown that the air also has received again exactly the same
amount of heat as it gave out during its compression ; and, hence,
it is now left in a condition the same as that in which it was at

* The centigrade thermometric scale is adopted throughout this paper.

198 CONGELATION AND LIQUEFACTION [29

the commencement of the first process. The only change which
has been produced then, is that a certain quantity of heat has
been abstracted from a small mass of water at 0°, and dispersed
through an indefinite mass at the same temperature, the small
mass having thus been converted into ice. This conclusion, it
may be remarked, might be deduced at once by the application,
to the freezing of water, of the general principle developed by
Carnot, that no work is given out when heat passes from one
body to another without a fall of temperature ; or rather by the
application of the converse of this, which of course equally holds
good, namely that no work requires to be expended to make heat
pass from one body to another at the same temperature.

Next, to prove that the freezing point of water is lowered by
an increase of the pressure to which the water is subjected : — Let
the imaginary cylinder and piston employed in the foregoing
demonstration, be again supposed to contain some air at 0°. Let
the bottom of the cylinder be placed in contact with the water of
an indefinitely large lake at 0° ; and let the air be subjected to
compression by pressure applied by the hand to the piston. A
certain amount of work is thus given from the hand to the air,
and a certain amount of heat is given out from the air to the
lake. Next, let the bottom of the cylinder be placed in commu-
nication with a small quantity of water at 0°, enclosed in a second
imaginary cylinder similar in character to the first, and which we
may call the water cylinder, the first being called the air cylinder;
and let this water be, at the commencement, subject merely to
the atmospheric pressure. Let, however, resistance be offered by
the hand to any motion of the piston of the water cylinder which
may take place. Things being in this state, let the piston of the
air cylinder move back to its original position. During this
process, heat becomes latent in the air on account of the increase
of volume, and therefore the air abstracts heat from the water,
because the air and water, being in communication with one
another, must remain each at the same temperature as the other,
whether that temperature changes or not. The first effect of the
abstraction of heat from the water must be the conversion of a
part of the water into ice, an effect which must be accompanied
with an increase of volume of the mass enclosed in the water
cylinder. Hence, on account of the resistance offered by the hand
to the motion of the piston of this cylinder, the internal pressure

1849] LOWERING OF THE FREEZING POINT OF WATER 199

is increased, and work is. received by the hand from the piston.
Towards the end of this process, let the resistance offered by the
hand gradually decrease, till, just at the end it becomes nothing,
and the pressure within the water cylinder thus becomes again
equal to that of the atmosphere. The temperature of the mass of
partly frozen water must now be 0°, and the air in the other
cylinder, being in communication with this, must have the same
temperature. The air is therefore at its original temperature,
and it has its original volume, or, in other words, it is in its
original state. Farther, let the ice be converted, under atmo-
spheric pressure, into water ; the requisite heat being transferred
to it from the lake by the mechanical process already pointed out,
which involves no loss of mechanical work. Thus, now at the
conclusion of the operation, the whole mass of water is left in its
original state ; and likewise, as has already been shown, the air is
left in its original state. Hence no work can have been developed
by any change on the air and water, which have been used. But
work has been given out by the piston of the water cylinder to
the hand; and therefore an equal quantity* of work must have
been given from the hand to the air piston, as there is no other
way in which the work developed could have been introduced into
the apparatus. Now, the only way in which this can have taken
place is by the air having been colder, while it was expanding in
the second process, than it was while it was undergoing com-
pression during the first. Hence it was colder than 0° during the
course of the second process ; or, in other words, while the water
was freezing, under a pressure greater than that of the atmo-
sphere, its temperature was lower than 0°.

The fact of the lowering of the freezing point being thus
demonstrated, it becomes desirable, in the next place, to find
what is the freezing point of water for any given pressure. The
most obvious way to determine this would be by direct experiment
with freezing water. I have not, however, made any attempt to
do so in this way. The variation to be appreciated is extremely
small, so small in fact as to afford sufficient reason for its existence
never having been observed by any experimenter. Even to
detect its existence, much more to arrive at its exact amount by
direct experiment, would require very delicate apparatus which

* In saying "an equal quantity" I, of course, neglect infinitely small quantities
in comparison to quantities not infinitely small.

200 CONGELATION AND LIQUEFACTION [29

would not be easily planned out or procured. Another, and a
better mode of proceeding has, however, occurred to me : and by
it we can deduce, from the known expansion of water in freezing,
and the known quantity of heat which becomes latent in the
melting of ice, together with data founded on the experiments of
Regnault on steam at the freezing point, a formula which gives
the freezing point in terms of t the pressure; and which may be
applied for any pressure, from nothing up to many atmospheres.
The following is the investigation of this formula.

Let us suppose that we have a cylinder of the imaginary
construction described at the commencement of this paper; and
let us use it as an ice-engine analogous to the imaginary steam-
engine conceived by Carnot, and employed in his investigations.
For this purpose, let the entire space enclosed within the cylinder
by the piston be filled at first with as much ice at 0° as would, if
melted, form rather more than a cubic foot of water, and let the
ice be subject merely to one atmosphere of pressure, no force
being applied to the piston. Now, let the following four processes,
forming one complete stroke of the ice-engine, be performed.

PROCESS 1. Place the bottom of the cylinder in contact with
an indefinite lake of water at 0°, and push down the piston. The
effect of the motion of the piston is to convert ice at 0° into water
at 0°, and to abstract from the lake at 0° the heat which becomes
latent during this change. Continue the compression till one
cubic foot of water is melted from ice.

PROCESS 2. Remove the cylinder from the lake, and place it
with its bottom on a stand which is a perfect non-conductor of
heat. Push the piston a very little farther down, till the pressure
inside is increased by any desired quantity which may be denoted,
in pounds on the square foot, by p. During this motion of the
piston, since the cylinder contains ice and water, the temperature
of the mixture must vary with the pressure, being at any instant
the freezing point which corresponds to the pressure at that
instant. Let the temperature at the end of this process be
denoted by - t° C.

PROCESS 3. Place the bottom of the cylinder in contact with
a second indefinitely large lake at — 1°, and move the piston
upwards. During this motion the pressure must remain constant
at p above that of the atmosphere, the water in the cylinder
increasing its volume by freezing, since if it did not freeze, its

1849] LOWERING OF THE FREEZING POINT OF WATER 201

pressure would diminish, and therefore its temperature would
increase, which is impossible, since the whole mass of water and
ice is constrained by the lake to remain at — 1°. Continue the
motion till so much heat has been given out to the second lake at
— 1°, as that if the whole mass contained in the cylinder were
allowed to return to its original volume without any introduction
or abstraction of heat, it would assume its original temperature
and pressure. This, if Carnot's principles be admitted, as they
are supposed to be throughout the present investigation, is the
same as to say, — Continue the motion till all the heat has been
given out to the second lake at — f, which was taken in during
Process 2, from the first lake at 0° *.

PROCESS 4. Remove the cylinder from the lake at — 1°, and
place its bottom again on the non-conducting stand. Move the
piston back to the position it occupied at the commencement of
Process 1. At the end of this fourth process the mass contained
in the cylinder must, according to the condition by which the
termination of Process 3 was fixed, have its original temperature
and pressure, and therefore it must bo in every respect in its
original physical state.

A G v >r >:

By representing graphically in a diagram the various volumes
and corresponding pressures, at all the stages of the four processes
which have just been described, we shall arrive, in a simple and
easy manner, at the quantity of work which is developed in one
complete stroke by the heat which is transferred during that
stroke from the lake at 0° to the lake at — 1°. For this purpose,

* [This is reprinted from Camb. and Dub. Math. Journal, Nov. 1850. In the
original paper, Trans. R.S. Edin., Jan. 1849, the last two sentences did not appear
except as regards the last three lines beginning with "continue" ; and the following
footnote appeared.

"This step, as well as the corresponding one in Carnot's investigation, it
must be observed, involves difficult questions, which cannot as yet be satisfactorily
answered, regarding the possibility of the absolute formation or destruction of heat
as an equivalent for the destruction or formation of other agencies, such as
mechanical work ; but, in taking it, I go on the almost universally adopted sup-
position of the perfect conservation of heat."]

202 CONGELATION AND LIQUEFACTION [29

let E be the position of the piston at the beginning of Process 1 ;
and let some distance, such as EG, represent its stroke in feet, its
area being made a square foot, so that the numbers expressing, in
feet, distances along EG may also express, in cubic feet, the
changes in the contents of the cylinder produced by the motion of
the piston. Now, when T087 cubic feet of ice are melted, one
cubic foot of water is formed. Hence, if EF be taken equal to
"087 feet, F will be the position of the piston when one cubic foot
of water has been melted from ice, that is, the position at the end
of Process 1, the bottom of the cylinder being at a point A
distant from F by rather more than a foot. Let FG be the
compression during Process 2, and HE the expansion during
Process 4. Let ef be parallel to EF, and let Ee represent one
atmosphere of pressure; that is, let the units of length for the
vertical ordinates be taken such that the number of them in Ee
may be equal to the number which expresses an atmosphere of
pressure. Also let gh be parallel to EF, and let fm represent the
increase of pressure produced during Process 2.

Then the straight lines ef and gh will be the lines of pressure
for Processes 1 and 3 ; and for the other two processes, the lines
of pressure will be some curves which would extremely nearly
coincide with the straight lines fg and he. For want of experi-
mental data, the natures of these two curves cannot be precisely
determined ; but, for our present purpose, it is not necessary that
they should be so, as we merely require to find the area of the
figure efgh, which represents the work developed by the engine
during one complete stroke, and this can readily be obtained with
sufficient accuracy. For, even though we should adopt a very
large value for fm, the change of pressure during Process 2, still
the changes of volume gm and hn in Processes 2 arid 4 would be
extremely small compared to the expansion during the freezing of
the water ; and from this it follows evidently that the area of the
figure efgh is extremely nearly equal to that of the rectangle
efmn, but fe is equal to FE which is '087 feet. Hence the work
developed during an entire stroke is '087 x p foot-pounds. Now
this is developed by the descent from 0° to — 1° of the quantity of
heat necessary to melt a cubic foot of ice; that is, by 4925
thermic units, the unit being the quantity of heat required to
raise a pound of water from 0° to 1° centigrade. Next we can
obtain another expression for the same quantity of work ; for, by

1849] LOWERING OF THE FREEZING POINT OF WATER 203

the tables deduced in the preceding paper* from the experiments
of Regnault, we find that the quantity of work developed by one
of the same thermic units descending through one degree about
the freezing point, is 4'97 foot-pounds. Hence, the work due to
4925 thermic units descending from 0° to - 1° is 4925 x 4'97 x t
foot-pounds. Putting this equal to the expression which was
formerly obtained for the work due to the same quantity of heat
falling through the same number of degrees, we obtain

4925 x497 x £=-087 xp.
Hence t = "00000355 p (1).

This, then, is the desired formula for giving the freezing point
— 1° centigrade, which corresponds to a pressure exceeding that of
the atmosphere by a quantity p, estimated in pounds on a square
foot.

To put this result in another form, let us suppose water to be
subjected to one additional atmosphere, and let it be required to
find the freezing point. Here p = one atmosphere = 2120 pounds
on a square foot; and therefore, by (1),

$ = •00000355x2120, or £ = '0075.

That is, the freezing point of water, under the pressure of one
additional atmosphere, is —'0075° centigrade; and hence, if the
pressure above one atmosphere be now denoted in atmospheres "f,
as units, by n, we obtain t, the lowering of the freezing point in
degrees centigrade, by the following formula,

£ = '0075n (2).

(The phenomena predicted by the author, in anticipation of
any direct observations on the freezing point of water, have been
fully confirmed by experiment. See a short paper published in
the Proceedings of the Royal Society of Edinburgh (Jan. 1850),
and republished in the Philosophical Magazine for August 1850,
under the title "The Effect of Pressure in Lowering the Freezing
Point of Water experimentally demonstrated. By Prof. William
Thomson." [Reprinted infra, No. 30.])

* [An Account of Carnot's Theory of the Motive Power of Heat', with Numerical
Results deduced from Regnault's Experiments on Steam. By William Thomson.
From the Transactions of the Royal Society of Edinburgh, xvi. 1849, p. 541. Bead
Jan. 2, 1849. Keprinted in Sir William Thomson's Mathematical and Physical
Papers, Vol. i. pp. 113—155, Art. XLI.]

t The atmosphere is here taken as being the pressure of a column of mercury of
760 millimetres; that is 29 -92, or very nearly 30 English inches.

204 CONGELATION AND LIQUEFACTION [30

30. THE EFFECT OF PRESSURE IN LOWERING THE FREEZING
POINT OF WATER EXPERIMENTALLY DEMONSTRATED. By
Professor WILLIAM THOMSON.

[From the Proc. R. S. E. Jan. 1850; Phil. Mag. xxxvu. 1850; Annal. de
Chimie, xxxv. 1852; Journ. de Pharm. xvm. 1850; Poggend. Annal.
LXXXI. 1850. Reprinted here from Sir William Thomson's (Lord
Kelvin's) Mathematical and Physical Papers, Vol. i. p. 165, Art. XLV.]

ON the 2nd of January 1849, a communication entitled
"Theoretical Considerations on the Effect of Pressure in Lowering
the Freezing Point of Water, by James Thomson, Esq., of
Glasgow," was laid before the Royal Society, and it has since been
published in the Transactions, Vol. xvi. part 5*. In that paper
it was demonstrated that, if the fundamental axiom of Carnot's
Theory of the Motive Power of Heat be admitted, it follows, as a
rigorous consequence, that the temperature at which ice melts
will be lowered by the application of pressure ; and the extent of
this effect due to a given amount of pressure was deduced by a
reasoning analogous to that of Carnot from Regnault's experi-
mental determination of the latent heat, and the pressure of
saturated aqueous vapour at various temperatures differing very
little from the ordinary freezing point of water. Reducing to
Fahrenheit's scale the final result of the paper, we find

t = nx 0-0135;

where " t " denotes the depression in the temperature of melting
ice produced by the addition of n " atmospheres " (or n times
the pressure due to 29*922 inches of mercury) to the ordinary
pressure experienced from the atmosphere.

In this very remarkable speculation, an entirely novel physical
phaenomenon was predicted in anticipation of any direct experi-
ments on the subject ; and the actual observation of the phae-
nomenon was pointed out as a highly interesting object for
experimental research.

To test the phaenomenon by experiment without applying
excessively great pressure, a very sensitive thermometer would be
required, since for ten atmospheres the effect expected is little

* It will appear also, with some slight alterations made by the author, in the
Cambridge and Dublin Mathematical Journal, November 1850. [See supra, p. 196.]

1850] LOWERING OF THE FREEZING POINT OF WATER 205

more than the tenth part of a Fahrenheit degree; and the
thermometer employed, if founded on the expansion of a liquid in
a glass bulb and tube, must be protected from the pressure of the
liquid, which, if acting on it, would produce a deformation, or at
least a compression of the glass that would materially affect the
indications. For a thermometer of extreme sensibility, mercury
does not appear to be a convenient liquid; since, if a very fine
tube be employed, there is some uncertainty in the indications on
account of the irregularity of capillary action, due probably to
superficial impurities, and observable even when the best mercury
that can be prepared is made use of; and again, if a very large
bulb be employed, the weight of the mercury causes a deformation
which will produce a very marked difference in the position of the
head of the column in the tube according to the manner in which
the glass is supported, and may therefore affect with uncertainty
the indications of the instrument. The former objection does not
apply to the use Of any fluid which perfectly wets the glass ; and
the last-mentioned source of uncertainty will be much less for any
lighter liquid than mercury, of equal or greater expansibility by
heat. Now the coefficient of expansion of sulphuric aether at
0°C. being, according to Mr I. Pierre*, '00151, is eight or nine
times that of mercury (which is '000179, according to Regnault),
and its density is about the twentieth part of the density of
mercury. Hence a thermometer of much higher sensibility may
be constructed with aether than with mercury, without experiencing
inconvenience from the circumstances which have been alluded
to. An aether thermometer was accordingly constructed by
Mr Robert Mansell of Glasgow, for the experiment which I
proposed to make. The bulb of this instrument is nearly cylin-
drical, and is about 3^ inches long and 3/8ths of an inch in
diameter. The tube has a cylindrical bore about 6J inches long :
about 5£ inches of the tube are divided into 220 equal parts.
The thermometer is entirely inclosed, and hermetically sealed in
a glass tube, which is just large enough to admit it freely f. On

* See Dixon, On Heat, p. 72.

t Following a suggestion made to me by Professor Forbes of Edinburgh, I have
in subsequent experiments with this thermometer used it with enough of mercury
introduced into the tube in which it is hermetically sealed to entirely cover its
bulb ; as I found that, without this, if the experiment was conducted in a warm
room, the indications of the thermometer were frequently deranged by the portion
of the water which was left free from ice becoming slightly elevated in temperature.

206 CONGELATION AND LIQUEFACTION [30

comparing the indications of this instrument with those of a
thermometer of Crichton's with an ivory scale, which has divisions
corresponding to degrees Fahrenheit of about l/25th of an inch
each, I found that the range of the aether thermometer is about
3° Fahrenheit; and that there are about 212 divisions on the tube
corresponding to the interval of temperature from 31° to 34°, as
nearly as I could discover from such an unsatisfactory standard of
reference. This gives 1/71 of a degree for the mean value of a
division. From a rough calibration of the tube which was made,
I am convinced that the values of the divisions at no part of the
tube differ by more than l/30th of this amount from the* true
mean value; and, taking into account all the sources of uncertainty,
I think it probable that each of the divisions on the tube of the
aether thermometer corresponds to something between 1/68 and
1/75 of a degree Fahrenheit.

With this thermometer in its glass envelope, and with a
strong glass cylinder (CErsted's apparatus for the compression of
water), an experiment was made in the following manner :

The compression vessel was partly filled with pieces of clean
ice and water : a glass tube about a foot long and l/10th of an
inch internal diameter, closed at one end, was inserted with its
open end downwards, to indicate the fluid pressure by the com-
pression of the air which it contained; and the aether thermometer
was let down and allowed to rest with the lower end of its glass
envelope pressing on the bottom of the vessel. A lead ring was
let down so as to keep free from ice the water in the compression
cylinder round that part of the thermometer tube where readings
were expected. More ice was added above ; so that both above
and below the clear space, which was only about two inches deep,
the compression cylinder was full of pieces of ice. Water was
then poured in by a tube with a stopcock fitted in the neck of the
vessel, till the vessel was full up to the piston, after which the
stopcock was shut.

After it was observed that the column of aether in the
thermometer stood at about 67°, with reference to the divisions
on the tube, a pressure of from 12 to 15 atmospheres was applied,
by forcing the piston down with the screw. Immediately the
column of aether descended very rapidly, and in a very few
minutes it was below 61°. The pressure was then suddenly
removed, and immediately the column in the thermometer began

1850] LOWERING OF THE FREEZING POINT OF WATER 207

to rise rapidly. Several times pressure was again suddenly
applied, and again suddenly removed, and the effects upon the
thermometer were most marked.

The fact that the freezing point of water is sensibly lowered
by a few atmospheres of pressure was thus established beyond all
doubt. After that I attempted, in a more deliberate experiment,
to determine as accurately as my means of observation allowed
me to do, the actual extent to which the temperature of freezing
is affected by determinate applications of pressure.

In the present communication I shall merely mention the
results obtained, without entering at all upon the details of the
experiment.

I found that a pressure of, as nearly as I have been able to
estimate it, 8'1 atmospheres produced a depression measured by
7J divisions of the tube on the column of aether in the thermo-
meter; and again, a pressure of 16'8 atmospheres produced a
thermometric depression of 16 J divisions. Hence the observed
lowering of temperature was 7^/71, or '106° F. in the former case,
and 16i/7l, or '232° F. in the latter.

Let us compare these results with theory. According to the
conclusions arrived at by my brother in the paper referred to
above, the lowering of the freezing point of water by 81 atmo-
spheres of pressure would be 8'1 x '0135, or 109° F., and the
lowering of the freezing point by 16'8 atmospheres would be
16'8 x -0135, or '227° F. Hence we have the following highly
satisfactory comparison, for the two cases, between the experiment
and theory :

Depressions according to
Observed de- theory, on the hypo-
pressions of thesis that the pressures
Observed pressures temperatures were truly observed Differences

8-1 atmospheres -106° F. -109° F. - -003° F.

16-8 atmospheres -232° F. -227° F. +-005° F.

It was, I confess, with some surprise, that, after having com-
pleted the observations under an impression that they presented
great discrepancies from the theoretical expectations, I found the
numbers I had noted down indicated in reality an agreement so
remarkably close, that I could not but attribute it in some degree
to chance, when I reflected on the very rude manner in which the
quantitative parts of the experiment (especially the measurement

208 CONGELATION AND LIQUEFACTION [31

of the pressure, and the evaluation of the division of the aether
thermometer) had been conducted.

I hope before long to have a thermometer constructed, which
shall be at least three times as sensitive as the aether thermo-
meter I have used hitherto ; and I expect with it to be able to
perceive the effect of increasing or diminishing the pressure by
less than an atmosphere, in lowering or elevating the freezing
point of water.

If a convenient minimum thermometer could be constructed,
the effects of very great pressures might easily be tested by
hermetically sealing the thermometer in a strong glass, <5r in a
metal tube, and putting it into a mixture of ice and water, in a
strong metal vessel, in which an enormous pressure might be
produced by the forcing-pump of a Bramah's press.

In conclusion, it may be remarked, that the same theory which
pointed out the remarkable effect of pressure on the freezing
point of water, now established by experiment, indicates that a
corresponding effect may be expected for all liquids which expand
in freezing ; that a reverse effect, or an elevation of the freezing
point by an increase of pressure, may be expected for all liquids
which contract in freezing ; and that the extent of the effect to be
expected may in every case be deduced from Kegnault's observations
on vapour (provided that the freezing point is within the tem-
perature-limits of his observations), if the latent heat of a cubic
foot of the liquid, and the alteration of its volume in freezing be
known. .

31. ON THE PLASTICITY OF ICE, AS MANIFESTED IN GLACIERS.

[From the Proceedings of the Royal Society, Vol. vni. 1856 — 7, p. 455.
Received April 1st, 1857, read May 7th, 1857.]

THE object of this communication is to lay before the Royal
Society a theory which I have to propose for explaining the
plasticity of ice at the freezing point, which is shown by observa-
tions by Professor James Forbes, and which is the principle of his
Theory of Glaciers.

1857J ON THE PLASTICITY OF ICE IN GLACIERS 209

This speculation occurred to me mainly in or about the year
1848. I was led to it from a previous theoretical deduction at
which I had arrived, namely, that the freezing point of water, or
the melting point of ice, must vary with the pressure to which
the water or the ice is subjected, the temperature of freezing or
melting being lowered as the pressure is increased. My theory
on that subject is to be found in a paper by me, entitled "Theo-
retical Considerations on the Effect of Pressure in Lowering the
Freezing Point of Water," published in the Transactions of the
Royal Society of Edinburgh, Vol. xvi. part 5, 1849*. It is there
inferred that the lowering of the freezing point, for one additional
atmosphere of pressure, must be '0075° centigrade ; and that if
the pressure above one atmosphere be denoted in atmospheres as
units by n, the lowering of the freezing point, denoted in degrees
centigrade by t, will be expressed by the formula t = '0075 n.

The phenomena which I there predicted, in anticipation of
direct observations, were afterwards fully established by experi-
ments made by my brother, Professor William Thomson, and
described in a paper by him, published in the Proceedings of the
Royal Society of Edinburgh (Jan. 1850) under the title "The
Effect of Pressure in Lowering the Freezing Point of Water
Experimentally Demonstrated •(•."

The principle of the lowering of the freezing point by pressure
being laid down as a basis, I now proceed to offer my explanation,
derived from it, of the plasticity of ice at the freezing point as
follows : —

If to a mass of ice at 0° centigrade, which may be supposed at
the outset to be slightly porous, and to contain small quantities of
liquid water diffused through its substance, forces tending to change
its form be applied, whatever portions of it may thereby be subjected
to compression will instantly have their melting point lowered so
as to be below their existing temperature of 0° cent. Melting of
those portions will therefore set in throughout their substance, and
this will be accompanied by a fall of temperature in them on
account of the cold evolved in the liquefaction. The liquefied
portions being subjected to squeezing of the compressed mass in
which they originate, will spread themselves out through the
pores of the general mass, by dispersion from the regions of
greatest to those of least fluid pressure. Thus the fluid pressure

* [Supra, p. 196.] t [Supra, p. 204.]

T. 14

210 CONGELATION AND LIQUEFACTION [31

is relieved in those portions in which the compression and lique-
faction of the ice had set in, accompanied by the lowering of
temperature. On the removal of this cause of liquidity — the
fluid pressure, namely — the cold which had been evolved in the
compressed parts of the ice and water, freezes the water again in
new positions, and thus a change of form, or plastic yielding of
the mass of ice to the applied pressures, has occurred. The newly
formed ice is at first free from the stress of the applied forces, but
the yielding of one part always leaves some other part exposed to
the pressure, and that, in its turn, acts in like manner ; and on
the whole, a continual succession goes on of pressures being
applied to particular parts — liquefaction in those parts — dispersion
of the water so produced in such directions as will relieve its
pressure, — and recongelation, by the cold previously evolved, of
the water on its being relieved from this pressure. Thus the
parts recongealed after having been melted must, in their turn,
through the yielding of other parts, receive pressures from the
applied forces, thereby to be again liquefied, and to enter again
on a similar cycle of operations. The succession of these processes
must continue as long as the external forces tending to change of
form remain applied to the mass of porous ice permeated by
minute quantities of water.

Postscript received 22nd April, 1857.

It will be observed that in the course of the foregoing com-
munication, I have supposed the ice under consideration to be
porous, and to contain small quantities of liquid water diffused
through its substance. Porosity and permeation by liquid water
are generally understood, from the results of observations, and
from numerous other reasons, to be normal conditions of glacier
ice. It is not, however, necessary for the purposes of my explana-
tion of the plasticity of ice at the freezing point, that the ice
should be at the outset in this condition ; for, even if we commence
with the consideration of a mass of ice perfectly free from porosity,
and free from particles of liquid water diffused through its
substance, and if we suppose it to be kept in an atmosphere at or
above 0° centigrade, then, as soon as pressure is applied to it,
pores occupied by liquid water must instantly be formed in the
compressed parts in accordance with the fundamental principle of
the explanation which I have propounded — the lowering, namely,

1857] ON THE PLASTICITY OF ICE IN GLACIERS 211

of the freezing or melting point by pressure, and the fact that ice
cannot exist at 0° cent, under a pressure exceeding that of the
atmosphere. I would also wish to make it distinctly understood
that no part of the ice, even if supposed at the outset to be solid
or free from porosity, can resist being permeated by the water
squeezed against it from such parts as may be directly subjected
to the pressure, because the very fact of that water being forced
against any portions of the ice supposed to be solid will instantly
subject them to pressure, and so will cause melting to set in
throughout their substance, thereby reducing them immediately
to the porous condition.

Thus it is a matter of indifference as to whether we commence
with the supposition of a mass of porous or of solid ice.

[The following paragraph was added to the paper as read in August 1857
at the Dublin meeting of the British Association. See Report, Part n. p. 40.]

Mr Thomson then referred to an experiment made by Prof.
Christie, late Secretary to the Royal Society, showing the plas-
ticity of ice in small hand specimens, and also to more recent
experiments by Prof. Tyndall to the same effect, and very
interesting on account of the striking way in which they exhibit
the phenomena. He also stated that another very important
quality of ice was brought forward by Faraday in 1850 (see
Athenaeum, No. 1181). It was that two pieces of moist ice will
consolidate into one on being laid in contact with one another,
even in hot weather. The theory he had just propounded, he
said, afforded a clear explanation of this fact as follows : — The two
pieces of ice, on being pressed together at their point of contact,
will, at that place, in virtue of the pressure, be in part liquefied
and reduced in temperature, and the cold evolved in their lique-
faction will cause some of the liquid film intervening between the
two masses to freeze. It is thus evident, he added, that by
continued pressure fragmentary masses of ice may be moulded
into a continuous mass ; and a sufficient reason is afforded for the
reunion, found to occur in glaciers, of the fragments resulting from
an ice cascade, and for the mending of the crevasses or deep
fissures which result occasionally from their motion along their
uneven beds.

14—2

212 CONGELATION AND LIQUEFACTION [32

32. CORRESPONDENCE WITH PROF. FARADAY ON REGELATION*.
(Hitherto unpublished.)

To Professor Faraday.

6, FRANKLIN PLACE,
BELFAST, 30^ July 1858.

SIR,

At the request of my brother Professor William Thomson of
Glasgow College, I take the liberty of sending to you the enclosed
abstract of a Paper " On the Effect of Pressure in Lowering the
Freezing Point of Water and on the Plasticity of Ice f."

The theory explained in this paper, as you will observe by a
clause near the conclusion of the abstract j, I consider affords a
satisfactory explanation of the interesting property of ice to which
you directed attention, that separate masses of ice laid in contact
with one another will, even in hot weather, unite or freeze firmly
together.

I am Sir Your obedient servant

JAMES THOMSON.

To Professor James Thomson.

ROYAL INSTITUTION,

4 August 1858.

MY DEAR SIR,

I receive it as very kind of you that you should send me
the Belfast report of your paper on Ice etc. I knew of, and have
been very much interested with, your views respecting ice, and
the effect generally of pressure on the fusing point. Prof. W.
Thomson told me of them long ago.

All the reasoning in the report I accept as truth ; though
I may hesitate in supposing that it contains the whole of what
concerns the assumption of the solid or the liquid state by a
particle of water under given circumstances.

* [As regards this and some of the following sections reference should be made
to Faraday's Experimental Researches in Chemistry and Physics, 1859, as follows : —

" On Certain Conditions of Freezing Water," a Royal Institution discourse of
1850, pp. 372—4; "On Ice of Irregular Fusibility," a letter to Professor Tyndall,
Dec. 9, 1857, pp. 374—7; and a note "On Regelation," pp. 377—82 written for
the reprint in that volume. All are referred to in this correspondence.]

t [Read before the Belfast Natural History and Philosophical Society, 2nd Dec.,
1857. It comprised the substance of papers Nos. 29, 31, supra, pp. 196 and 208.]

J [Supra, p. 211.]

1858] CORRESPONDENCE WITH PROF. FARADAY ON REGELATION 213

It is curious and interesting to observe how much the general
question has drawn attention. Forbes is thinking about it — so is
Tyridall, and others also in Paris. The peculiar supposition of a
stickiness of the ice, at the freezing or solidifying point, is
interesting ; but one wants some better proof than, or additional
proof besides, the fact of regelation ; I have not worked at the
subject of late ; but I could not make ice stick to gold or metal at
32°, and I do not think that Forbes' shilling is any proof of it.

Being sure that your principle is correct, which requires
pressure and its variations; — and admitting stickiness, simply
because I am not prepared to deny it ; — I am at present strongly
of opinion that there is another efficient cause of regelation to
which I think I have referred in the old Athenaeum report : — but
I have not that here, and therefore cannot clearly say. It seems
to me that a particle of water, touching ice on one side and water
at the same temperature on the other, is not so apt to change its
state for that of ice as another touching ice on both sides ; — and
this, not as the consequence of any very limited peculiarity in
water and ice, but in subordination to a far more general law, if
I may so call it, that in bodies of the same kind the particles tend
to retain the state of those which surround them. Thus water
may be cooled many degrees below 32° F. but a particle of the
water in the midst of the cooled mass remains as water though
colder than ice : — and yet a warmer body than itself, as for
instance a spicule of ice, touching it on one side and so breaking
up the continuous liquid contact around it, instantly makes it
solidify.

In the same manner I can conceive that a particle of ice in the
middle of ice may be raised with the mass to a higher temperature,
before it become water, than a particle of the same ice at the
surface can, — this change from ice to water and water to ice
being independent of any effect of pressure.

We have an illustration of this effect in water also, when it
changes from the liquid to the gaseous state, instead of from the
liquid to the solid state. It is given us in Donny's beautiful
results ; where he shows that water, freed from air, may be heated
to I think 300° F. under the pressure of one atmosphere only, and
yet not boil or be converted into vapour within, though the intro-
duction of the minutest bubble of air will cause it to explode :—
a given liquid particle in the mass not being able at this high

214 CONGELATION AND LIQUEFACTION [32

temperature to change its state into that of vapour whilst in
contact on every side with liquid particles like itself, though if
once the contact of these particles be broken in any point, they
will burst with violence into the new state.

Great numbers of other cases of this kind may be found
amongst bodies able to change their state ; but they will readily
occur to you. I am about to reprint my report from the Athenaeum
in a volume of Experimental Researches on Physics; I think I
shall arrange these views into some kind of form so as to give
them a place beside your views and those of Forbes and others.
You have them, uncorrected by any experiments except those of
former time, for I have made none lately though I have seen
Tyndall's.

Believe me to be
My dear Sir

Most truly yours
M. FARADAY.

To Professor Faraday.

2 DONEGALL SQUARE WEST, BELFAST,

9th Nov. 1858.
MY DEAR SIR,

I thank you very much for having so kindly written
to me in August last on the subject of the freezing and melting
point of water and ice.

I intended to write to you at the time, thanking you for your
letter ; but, through illness in my family, and repeated absences
from home on business, I have hitherto found myself detained
from reverting to the subject.

I recollect that in the old Athenaeum report of your Paper — to
which however I have not had access of late — mention is made of
your supposition that there is a tendency for a film of water
between two surfaces of ice to become ice, other particles touching
ice only on one side becoming water at the same time, and
supplying the cold necessary to freeze the water between the two
surfaces of ice. Having been long aware of that supposition, and
now having farther had your letter of Aug. 4 to consider, I still
incline to think that the freezing of the film between the two
masses of ice is due simply to the melting by pressure of portions
of the ice pressed against one another at places of contact.

1858] CORRESPONDENCE WITH PROP. FARADAY ON REGELATION 215

Soon after the time when I received your letter, I met with a
paper by Prof. Forbes of Edinburgh (from the Proceedings of the
Royal Society of Edinburgh dated the 19th of April 1858) " On
Properties of Ice near its Melting Point." This I presume to be
the paper in which his shilling experiment is mentioned to which
you alluded in your letter to me. In that paper Forbes states an
experiment as proving that two masses of ice placed extremely
close together, and having a film of water intervening, but free
from pressure against one another, will unite even in a moderately
warm atmosphere. I am not, however, prepared to admit the
validity of his proof in this matter. He had slight springs pressing
the masses of ice together : but beyond this I conceive that the
capillary attraction of the intervening water would draw the
masses against one another with a force quite notable ; — and also
I conceive that the film of water between the two masses of ice
would be sustained almost entirely by capillary attraction at its
upper surface, and would therefore exist (like mercury in a
barometer) under a pressure less than that of the atmosphere.
This diminished fluid pressure would raise the freezing point of
the film of water, and would produce a tendency to its freezing,
even by contact with such parts of the adjacent ice as exist under
atmospheric pressure, — and much more by contact with the parts
of the two masses of ice in contact with one another and pressing
against one another by the forces of the spring used to maintain
contact and of the capillary attraction of the fluid pulling the
masses against one another. Thus I still incline to think that
mere proximity is not enough to cause the two pieces of ice to
unite.

In your letter to me you make reference, as bearing on this
subject, to what appears to be a very general law, namely that, in
bodies of the same kind, the particles tend to retain the state of
those which surround them : — as, for instance, that water may be
cooled much below 32° F. without freezing, but that a spicule of
ice touching it will instantly make it solidify: and that water
may be raised under atmospheric pressure to a temperature far
above 212° F. without boiling, but that a bubble of air introduced
will cause it to explode. It seems to me, however, that these
phenomena are essentially distinct from what can occur with a
film of water touching ice on one side, or on two opposite sides,
because, in the phenomena you adduce, the tendency is for a

216 CONGELATION AND LIQUEFACTION [32

particle to retain a state in which it already exists, that state
being the same as the state of the surrounding ones: but I do not
think they show a tendency for a particle differing in its state
from the surrounding particles to assume their state. It is certain
that, in numerous cases, every particle shows a great resistance to
change from a state in which it and all adjacent particles exist.
In the case of a film of water between two masses of ice, however,
the difficulty of making a beginning either of melting or freezing
does not exist, as both water and ice are present together.

I do not see in the principle I have proposed any insufficiency
to explain the regelation of fractured ice, and the plasticit^ of ice ;
and, according to the views I have just now submitted, I do not
see that we ought to suppose the occurrence of another efficient
cause of regelation, such as you have suggested.

With great deference I beg to offer the above remarks to
you.

I am, with thanks, yours most truly,

JAMES THOMSON.

P.S. It may be well to mention that I conceive the powerful
tendency to adhesion manifested between flannel and ice in a
warm atmosphere, is to be attributed partly to the fibres of the
flannel being drawn against the ice by capillary attraction of the
liquid films, and thus being made to apply a pressure to the ice
which must slightly lower its melting point ; and again partly to
the diminished fluid pressure of the liquid films produced by
capillary attraction, which must raise the freezing point of those
films. J. T.

To Professor James Thomson.

ALBEMARLE STREET, W.

15 Nov. 1858.
MY DEAR SIR,

I am much obliged by your note. I happen to be
occupied in collecting my papers (not electrical) into a volume, and
on reprinting the notice on ice from the Athenaeum have added a
further development of my views : — it will come out in the course
of the winter I dare say, but that is as the printer likes.

You represent that my view gives no account of the beginning
of the regelation. That is not so great a difficulty to my mind as

1858] CORRESPONDENCE WITH PROF. FARADAY ON REGELATION 21*7

to yours ; because, since the year 1833, if not before that time,
I have been obliged to admit that particles cannot be so exclusively
engaged, even by a combining chemical action, as to be indifferent
to, or without relation to, those alongside of them.

I will mention a difficulty as regards this beginning of regela-
lation which occurs to me under your view, if the particles be
supposed to be without this external relation. You admit with me
that bodies tend to retain that state which they for the time
possess; and that against a change of temperature of many
degrees of heat; — then how can the small change of temperature
not amounting to the -^th of a degree, due to difference of
pressure in many of the regelation experiments, cause that
change from solid to fluid, or fluid to solid, which many degrees
of temperature change, applied in the common way, will not
effect ?

It seems that in ice the melting temperature is irregular, i.e.
that certain portions of the ice tend to melt before other portions.
I have given my view of this irregularity in a note, which Tyndall
has added to his last paper in the Phil. Trans. : —

If ice of equal purity should, either from crystalline arrange-
ment or some other cause, prove to be a mixture of particles
having differences in their fusibility, then it would be very easy
to build up a fourth theory of regelation. But time, reconsidera-
tion, new thoughts and new experiments, will no doubt clear up
all these matters.

Ever my dear Sir,

Very truly yours,

M. FARADAY.

To Professor Faraday.

2 DONEGALL SQUARE WEST, BELFAST,

24*A Nov. 1858.

MY DEAR SIR,

I am much obliged for your letter of the 15th inst.; and
I presume I have to thank you and Prof. Tyndall jointly for a copy
of his paper containing the note from you appended, which he has
kindly sent to me and of which the contents interest me much.

There was hard frost here last night: and having happened
to meet with slabs of ice about 1J inch thick, I have repeated

218

CONGELATION AND LIQUEFACTION

[32

Forbes' experiment of suspending two slabs of ice on a horizontal
glass rod thus : —

GlassAod

I found that in a few hours (during which water was constantly
dropping from them) the two slabs were stuck fast together — and
I did not find it necessary to apply springs to produce any
pressure at all. I merely pressed them gently with my hands for
a few seconds at first, to make them keep close together by an
incipient cohesion or a cohesion of some minute spots. The
cohesion then went on increasing till in a few hours it became
very strong. Although there is no spring necessary, yet the
capillary attraction due to the films of water between the two
plates, alluded to in my last letter to you, must keep up a steady
force, drawing the plates together and causing pressure at some
parts. I could see many square
inches of films of water between
the two plates or slabs of ice.

This water, being situated as
at a, a, a, a, a, a, in the figure,
must exist, by virtue of capillary
attraction, under less than atmos-
pheric pressure at all parts of
itself. This diminished pressure
must tend to cause the water to
freeze even at a temperature
slightly above the ordinary freez-
ing point. The diminished pressure in the liquid film, extending
over several square inches, will cause the external atmospheric
pressure to force the two slabs against one another with quite
a notable force.

1858] CORRESPONDENCE WITH PROF. FARADAY ON REGELATION 219

It seems to me that you have somewhat misconceived my
meaning in respect to a " difficulty of making a beginning " as
you say in your last letter : —

" I will mention a difficulty as regards this beginning of rege-
lation which occurs to me under your view, if the particles be
supposed to be without this external relation. You admit with me
that bodies tend to retain that state which they for the time
possess; and that against a change of temperature of many
degrees of heat ; — then how can the small change of temperature
not amounting to the y^th of a degree, due to the difference of
pressure in many of the regelation experiments, cause that
change from solid to fluid, or fluid to solid, which many degrees
of temperature change, applied in the common way, will not
effect ? "

With reference to this I would say, that I think the resistance
to change of state from liquid to solid, or solid to liquid, or liquid
to gaseous, or gaseous to liquid, under consideration, occurs only
when the substance is not present in the two states already (as
for instance when water is cooled below 32° F., without freezing,
there is no ice present) but when both water and ice are in
contact, as is the case in the regelation experiments, it is a part
of my theory to suppose that there is no tendency for water to
remain water, or ice to remain ice, against any change of tempera-
ture however slight tending to change the state of the water or
the ice.

I shall look with much interest to the ideas given in your
note annexed to Prof. Tyndall's paper, and to the suggestion you
give in your last letter to me of a '' fourth theory of regelation "
as being perhaps possible to be built up.

I am, My dear Sir,

Very truly yours,

JAMES THOMSON.

220

CONGELATION AND LIQUEFACTION

[33

33. ON TUBULAR POKES IN ICE FROZEN ON STILL WATER.

[A paper on this subject was read before the Belfast Natural History and
Philosophical Society on the 20th April 1864, of which no report has
been preserved. The following letter to Professor William Thomson,
written on the 19th Feb. 1862, gives the substance of his explanation,
with possible application to similar structures in rock.]

2 DONEGALL SQUARE WEST, *

BELFAST, 19th Feb. 1862.

MY DEAR WILLIAM,

Perhaps you may have noticed in slabs of ice frozen on
the surface of a pond or of any vessel of water, great numbers of
small vertical pipes or tubes usually smaller than a pin or a needle.
In fig. 1 I have represented these pipes.

Surface of the Ice

Fig. 1.

They seem to me to begin from a very small size at top and
usually to increase somewhat in diameter downwards.

The question occurred to me how these pipes or tubes origi-
nated. They seemed to contain air; and
I judged that they are produced by
bubbles of air expelled from the water
during its congelation : — that each pipe
is produced by one bubble which is
small at first, and which floats up against
the under surface of the ice : — that the
ice is prevented from growing at the - ~ - -

spot where the bubble touches it and so
excludes the water from touching it :
or that in fact the water cannot freeze to the ice at a spot where

1862] ON TUBULAR PORES IN ICE FROZEN ON STILL WATER 221

no water is in contact with it, but where the air of the bubble is
alone in contact with it : — that thus as the ice grows a tubular
opening is left behind the advancing round front of the bubble as
shown in fig. 2 or better in fig. 3 on a larger scale : — and that as
the ice goes on growing and the bubble in the water leaves a tail
of itself behind in the ice, new supplies of air are continually
expelled from the freezing water and added to the various bubbles;
so keeping up the supply of air to them during their growth
which keeps pace with the thickening ice.

Water

Fig. 3.

Dr Wyville Thomson happened to point out to me yesterday
some elongated vesicles in amygdaloidal trap rock. He remarked
on them as being of great interest, and supposed them to be formed
by streams of ascending bubbles. I think it very possible that
they may be explained on the same principle as the tubes in the
ice. What do you think of all this ? Have you ever seen the
tubes in the ice described or explained ?

Your affectionate brother,

JAMES THOMSON.

222 CONGELATION AND LIQUEFACTION [34

34. ON RECENT THEORIES AND EXPERIMENTS REGARDING ICE
AT OR NEAR ITS MELTING POINT.

[From the Proceedings of the Royal Society, Vol. x. 1859, pp. 152—160.
Eead November 24, 1859.]

MY object in the following paper is to discuss briefly the
bearings of some of the leading theories of the plasticity and other
properties of ice at or near its melting point, on speculations on
the same subject advanced by myself*, and especially, to offer an
explanation of an experiment made by Professor James D. Forbes,
which to him and others has seemed to militate against the
theory proposed by me, but which, in reality, I believe to be in
perfect accordance with that theory.

In the year 1850, Mr Faraday f invited attention, in a scientific
point of view, to the fact that two pieces of moist ice, when placed
in contact, will unite together, even when the surrounding tem-
perature is such as to keep them in a thawing state. He
attributed this phenomenon to a property which he supposed ice
to possess, of tending to solidify water in contact with it, and of
tending more strongly to solidify a film or a particle of water
when the water has ice in contact with it on both sides than when
it has ice on only one side.

In January 1857, Dr Tyndall, in a paper (by himself and Mr
Huxley) read before the Royal Society and in a lecture delivered
at the Royal Institution, adopted this fact as the basis of a theory
by which he proposed to explain the viscosity or plasticity of ice,
or its capability of undergoing change of form, which was previously
known to be the quality in glaciers in virtue of which their
motion down their valleys is produced by gravitation. Designating
Mr Faraday's fact under the term " regelation," Dr Tyndall
described the capability of glacier ice to undergo changes of form,
as being not true viscosity, but as being the result of vast
numbers of successively occurring minute fractures, changes of

* Proceedings of Royal Society, May 1857. Also British Association Proceed-
ings, Dublin Meeting, 1857. Also Proceedings of Belfast Literary and Philosophical
Society, Dec. 2, 1857. [See supra, No. 31, p. 208.]

t Lecture by Mr Faraday at the Royal Institution, June 7, 1850 ; and Report of
that Lecture, Athenaeum, 1850, p. 640. [Footnote, supra, p. 212.]

1859] ICE AT OR NEAR ITS MELTING POINT 223

position of the fractured parts, and regelations of those parts in
their new positions. The terms fracture and regelation then came
to be the brief expression of his idea of the plasticity of ice. He
appears to have been led to deny the applicability of the term
viscosity through the idea that the motion occurs by starts, due to
the sudden fractures of parts in themselves not viscous or plastic.
The crackling, he pointed out might, according to circumstances,
be made up of separate starts distinctly sensible to the ear and to
the touch, or might be so slight and so rapidly repeated as to melt
almost into a musical tone. He referred to slight irregular
variations in the bending motion of the line marked by a row of
pins on a glacier, by Prof. Forbes, as being an indication of the
absence of any quality that could properly be called viscosity, and
of the occurrence of successive fractures arid sudden motions in a
material not truly viscous or plastic. I can only understand his
statements on this subject by supposing that he conceived the
material between the cracks to be rigid, or permanent in form,
when existing under strains within the limit of its strength, or
when strained less than to the point of fracture.

This theory appeared to me to be wrong*; and I then published,

* While the offering of my own theory as a substitute for Professor Tyndall's
views seems the best argument I can adduce against them, still I would point to
one special objection to his theory. No matter how fragile, and no matter how
much fractured a material may be, yet if its separate fractured parts be not
possessed of some property of internal mobility, I cannot see how a succession of
fractures is to be perpetuated. A heap of sand or broken glass will either continue
standing, or will go down with sudden falls or slips, after which a position of
repose will be attained ; and I cannot see how the addition of a principle of
reunion could tend to reiterate the fractures after such position of repose has been
attained. When these ideas are considered in connection with the fact that while
ice is capable of standing, without immediate fall, as the side of a precipitous
crevasse, or of lying without instantaneous slipping on a steeply sloping pan of a
valley, it can also glide along, with its surface nearly level, or very slightly inclined,
I think the improbability of the motion arising from a succession of fractures of
a substance having its separate parts devoid of internal mobility will become very
apparent. If, on the other hand, any quality of internal mobility be allowed in
the fragments between the cracks, a certain degree at least of plasticity or viscosity
is assumed in order to explain the observed plasticity or viscosity. That fractures —
both large and exceedingly small — both large at rare intervals, and small, mo-
mentarily repeated — do, under various circumstances, arise in the plastic yielding
of masses of ice, is, of course, an undoubted fact : but it is one which I regard not
as the cause, but as a consequence, of the plastic yielding of the mass in the
manner supposed in my own theory. It yields by its plasticity in some parts, until
other parts are overstrained and snap asunder, or perhaps also sometimes slide
suddenly past one another.

224 CONGELATION AND LIQUEFACTION [34

in a paper communicated to the Royal Society, a theory which
had occurred to me mainly in or about the year 1848, or perhaps
1850; but which, up till the date of the paper referred to, had
only been described to a few friends verbally. That theory of
mine may be sketched in outline as follows : — If to a mass of ice
at its melting point, pressures tending to change its form be
applied, there will be a continual succession of pressures applied
to particular parts — liquefaction occurring in those parts through
the lowering of the melting point by pressure — evolution of the
cold by which the so melted portions had been held in t}ie frozen
state — dispersion of the water so produced in such directions as
will afford relief to the pressure — and recongelation, by the cold
previously evolved, of the water on its being relieved from this
pressure : and the cycle of operations will then begin again ; for
the parts recongealed after having been melted, must in their
turn, through the yielding of other parts, receive pressures from
the applied forces, thereby to be again liquefied* and to proceed
through successive operations as before.

Professor Tyndall, in papers and lectures subsequent to the
publication of this theory, appears to adopt it to some extent, and to
endeavour to make its principles cooperate with the views he had
previously founded on Mr Faraday's fact of so-called "regelation*."

Professor James D. Forbes adopts Person's view, that the
dissolution of ice is a gradual, not a sudden process, and so far
resembles the tardy liquefaction of fatty bodies or of the metals,
which in melting pass through intermediate stages of softness or
viscosity. He thinks that ice must essentially be colder than
water in contact with it ; that between the ice and the water
there is a film varying in local temperature from side to side,
which may be called plastic ice, or viscid water ; and that through
this film heat must be constantly passing from the water to the
ice, and the ice must be wasting away, though the water be what
is called ice-cold.

* I suppose the term regelation has been given by Professor Tyndall as denot-
ing the second, or mending stage in his theory of "Fracture and regelation."
Congelation would seem to me the more proper word to use after fracture, as
regelation implies previous melting. If my theory of melting by pressure and
freezing again on relief of pressure be admitted, then the term regelation will come
to be quite suitable for a part of the process of the union of the two pieces of ice,
though not for the whole, which then ought to be designated as the process of
melting and regelation.

1859] ICE AT OR NEAR ITS MELTING POINT 225

There is a manifest difficulty in conceiving the possibility of
the state of things here described: and I cannot help thinking
that Professor Forbes has been himself in some degree sensible of
the difficulty ; for in a note of later date by a few months than
the paper itself, he amends the expression of his idea by a state-
ment to the effect that if a small quantity of water be enclosed in
a cavity in ice, it will undergo a gradual "regelation"', that is,
that the ice will in this case be gradually increased instead of
wasted. In reference to the first case, I would ask, — What
becomes of the cold of the ice, supposing there to be no communi-
cation with external objects by which heat might be added to or
taken from the water and ice jointly considered ? Does it go into
the water and produce viscidity beyond the limit of the assumed
thin film of viscid water at the surface of the ice ? Precisely a
corresponding question maybe put relatively to the second case —
that of the large quantity of ice enclosing a small quantity of
water in which the reverse process is assumed to occur. Next,
let an intermediate case be considered — that of a medium quantity
of water in contact with a medium quantity of ice, and in which
no heat, nor cold, practically speaking, is communicated to the
water or the ice from surrounding objects. This, it is to be
observed, is no mere theoretical case, but a perfectly feasible one.
The result, evidently, if the previously described theories be
correct, ought to be that the mixture of ice and water ought to
pass into the state of uniform viscidity. Prof. Forbes's own words
distinctly deny the permanence of the water and ice in contact in
their two separate states, for he says, " bodies of different tem-
peratures cannot continue so without interaction. The water
must give off heat to the ice, but it spends it in an insignificant
thaw at the surface, which therefore wastes even though the water
be what is called ice-cold." Now the conclusion arrived at,
namely, that a quantity of viscid water could be produced in the
manner described, is, I am satisfied, quite contrary to all experience.
No person has ever, by any peculiar application of heat to, or
withdrawal of heat from, a quantity of water, rendered it visibly
and tangibly viscid. We even know that water may be cooled
much below the ordinary freezing point and yet remain fluid.

Professor Forbes regards Mr Faraday's fact of regelation as
being one which receives its proper explanation through his
theory described above ; and, in confirmation of the supposition
T. 15

226 CONGELATION AND LIQUEFACTION [34

that ice has a tendency to solidify a film of water in contact with
it, and in opposition to the theory given by me, that the regelation
is a consequence of the lowering of the melting point in parts
pressed together, he adduces an experiment made by himself,
which I admit presents a strong appearance of proving the
influence of the ice in solidifying the water, to be not essentially
dependent on pressure. This experiment, however, I propose to
discuss and explain in the concluding part of the present paper.

Professor Forbes accepts my theory of the plasticity of ice as
being so far correct that it points to some of the causes which
may reasonably be considered, under peculiar circumstances, to
impart to a glacier a portion of its plasticity. In the rapid
alternations of pressure which take place in the moulding of ice
under the Bramah's press, it cannot, he thinks, be doubted that
the opinions of myself and my brother Prof. William Thomson are
verified*.

Mr Faraday, in his recently published Researches in Chemistry
and Physics, still adheres to his original mode of accounting
for the phenomenon he had observed, and for which he now adopts
the name " regelation " ; or, at least, while alluding to the views
of Prof. Forbes as possibly being admissible as correct, and to the
explanation offered by myself as being probably true in principle,
and possibly having a correct bearing on the phenomena of
regelation, he considers that the principle originally assumed by
himself may after all be the sole cause of the effect. The principle
he has in view, he then states as being, when more distinctly
expressed, the following : — " In all uniform bodies possessing
cohesion, i.e. being either in the liquid or the solid state, particles
which are surrounded by other particles having the like state with
themselves . tend to preserve that state, even though subject to
variations of temperature, either of elevation or depression, which,
if the particles were not so surrounded, would cause them instantly
to change their condition." Referring to water in illustration, he
says that it may be cooled many degrees below 32° Fahr., and
still retain its liquid state; yet that if a piece of the same chemical
substance — ice — at a higher temperature be introduced, the cold
water freezes and becomes warm. He points out that it is

* Forbes, " On the Becent Progress and Present Aspect of the Theory of Glaciers,"
p. 12 (being introduction to a volume of Occasional Papers on the Theory of
Glaciers), February 1859.

1859] ICE AT OR NEAR ITS MELTING POINT 227

certainly not the change of temperature which causes the freezing;
for the ice introduced is warmer than the water ; and he says he
assumes that it is the difference in the condition of cohesion
existing on the different sides of the changing particles which
sets them free and causes the change. Exemplifying, in another
direction, the principle he is propounding, he refers to the fact
that water may be exalted to the temperature of 270° Fahr., at
the ordinary pressure of the atmosphere, and yet remain water ;
but that the introduction of the smallest particle of air or steam
will cause it to explode, and at the same time to fall in tempera-
ture. He further alludes to numerous other substances — such as
acetic acid, sulphur, phosphorus, alcohol, sulphuric acid, ether,
and camphine — which manifest like phenomena at their freezing
or boiling points, to those referred to as occurring with the
substance of water, ice, and steam ; and he adverts to the observed
fact that the contact of extraneous substances with the particles
of a fluid usually sets these particles free to change their state, in
consequence, he says, of the cohesion between them and the fluid
being imperfect ; and he instances that glass will permit water to
boil in contact with it at 212° Fahr., or by preparation can be
made so that water will remain in contact with it at 270° Fahr.
without going off into steam ; also that glass can be prepared so
that water will remain in contact with it at 22° Fahr. without
solidification, but that an ordinary piece of glass will set the water
off at once to freeze.

He afterwards comes to a point in his reasoning which he
admits may be considered as an assumption. It is "that many
particles in a given state exert a greater sum of their peculiar
cohesive force upon a given particle of the like substance in
another state than few can do ; and that as a consequence a water
particle with ice on one side, and water on the other, is not so apt
to become solid as with ice on both sides ; also that a particle of
ice at the surface of a mass (of ice) in water is not so apt to
remain ice as when, being within the mass there is ice on all
sides, temperature remaining the same." This supposition evi-
dently contains two very distinct hypotheses. The former, which
has to do with ice and water present together, I certainly do
regard as an assumption, unsupported by any of the phenomena
which Mr Faraday has adduced. The other, which has to do with
a particle of ice in the middle of continuous ice, and which

15—2

228 CONGELATION AND LIQUEFACTION [34

assumes that it will not so readily change to water, as another
particle of ice in contact with water, I think is to be accepted as
probably true. I think the general bearing of all the phenomena
he has adduced is to show that the particles of a substance when
existing all in one state only, and in continuous contact with one
another, or in contact only under special circumstances with other
substances, experience a difficulty of making a beginning of their
change of state, whether from liquid to solid, or from liquid to
gaseous, or probably also from solid to liquid : but I do not think
anything has been adduced showing a like difficulty as^to their
undergoing a change of state, when the substance is present in
the two states already, or when a beginning of- the change has
already been made. I think that when water and ice are present
together, their freedom to change their state on the slightest
addition or abstraction of heat, or the slightest change of pressure,
is perfect. I therefore cannot admit the validity of Mr Faraday's
mode of accounting for the phenomena of regelation.

Thus the fact of regelation which Prof. Tyndall has taken as
the basis of his theory for explaining the plasticity of ice, does in
my opinion as much require explanation as does the plasticity of
ice which it is applied to explain. The two observed phenomena,
namely the tendency of the separate pieces of ice to unite when in
contact, and the plasticity of ice, are indeed, as I believe, cognate
results of a common cause. They do not explain one another.
They both require explanation ; and that explanation, I consider,
is the same for both, and is given by the theory I have myself
offered.

I now proceed to discuss the experiment by Prof. Forbes,
already referred to as having been adduced in opposition to my
theory. He states that mere contact without pressure is sufficient
to produce the union of two pieces of moist ice* ; and then states,
as follows, his experiment by which he supposes that this is
proved : — " Two slabs of ice, having their corresponding surfaces
ground tolerably flat, were suspended in an inhabited room upon
a horizontal glass rod passing through two holes in the plates of
ice, so that the plane of the plates was vertical. Contact of the
even surfaces was obtained by means of two very weak pieces of
watch-spring. In an hour and a half the cohesion was so complete,

* " On some Properties of Ice near its Melting-Point," by Prof. Forbes,
Proceedings of the Royal Society of Edinburgh, April 1858.

1859] ICE AT OR NEAR ITS MELTING POINT 229

that, when violently broken in pieces, many portions of the plates
(which had each a surface of twenty or more square inches)
continued united. In fact it appeared as complete as in another
experiment where similar surfaces were pressed together by
weights." He concludes that the effect of pressure in assisting
" regelation " is principally or solely due to the larger surfaces of
contact obtained by the moulding of the surfaces to one another.

I have myself repeated this experiment, and have found the
results just described to be fully verified. It was not even
necessary to apply the weak pieces of watch-spring, as I found
that the pieces of ice, on being merely suspended on the glass rod
in contact, would unite themselves strongly in a few hours. Now
this fact I explain by the capillary forces of the film of interposed
water as follows: — Firstly, the film of water between the two slabs
—being held up against gravity by the capillary tension, or con-
tractile force, of its free upper surface, and being distended besides,
against the atmospheric pressure, by the same contractile force of
its free surface round its whole perimeter, except for a very small
space at bottom, from which water trickles away, or is on the
point of trickling away — exists under a pressure which, though
increasing from above downwards, is everywhere, except at that
little space at bottom, less than the atmosphere pressure. Hence
the two slabs are urged towards one another by the excess of the
external atmospheric pressure above the internal water pressure,
and are thus pressed against one another at their places of contact
by a force quite notable in its amount. If, for instance, between
the two slabs there be a film of water of such size and form as
might be represented by a film one inch square, with its upper
and lower edges horizontal, and with water trickling from its
lower edge, it is easy to show that the slabs will be pressed
together by a force equal to the weight of half a cubic inch of
water. But so small a film as this would form itself even if the two
surfaces of the ice were only very imperfectly fitted to one another.
If, again, by better fitting, a film be produced of such size and form
as may be represented by a square film with its sides four inches
each, the slabs will be urged together by a force equal to the
weight of half a cube of water of which the side is four inches ;
that is, the weight of 32 cubic inches of water or 1*15 pound,
which is a very considerable force. Secondly, the film of water
existing, as it does, under less than atmospheric pressure, has its

230 CONGELATION AND LIQUEFACTION [35

freezing point raised in virtue of the reduced pressure ; and it
would therefore freeze even at the temperature of the surrounding
ice, namely the freezing point for atmospheric pressure. Much
more will it freeze in virtue of the cold given out in the melting
by pressure of the ice at the points of contact, where, from the
first two causes named above, the two slabs are urged against one
another.

The freezing of ice to flannel or to a worsted glove on a warm
hand is, I consider, to be attributed' partly to capillary attraction
acting in similar ways to those just described; but in many of
the observed cases of this phenomenon there will also be direct
pressures from the hand, or from the weight of the ice, or from
other like causes, which will increase the rapidity of the moulding
of the ice to the fibres of the wool.

[This paper was also read at the British Association meeting at Aberdeen,
September 1859.]

35. NOTE ON PROFESSOR FARADAY'S RECENT EXPERIMENTS
ON "REGELATION."

[From the Proceedings of the Royal Society, April 25, 1861, Vol. xi. p. 198.
Also Phil. Mag. Fourth Series, Vol. xxm. (1862), pp. 407, 411.]

SOME time ago*, Principal James D. Forbes showed that two
slabs of ice, having each a face ground tolerably flat, and being
both suspended in an atmosphere a little above the freezing point
upon a horizontal rod of glass passed through two holes in the
plates of ice, so that the plates might hang vertically and in
contact with one another, would unite gradually so as to adhere
strongly together. This interesting experiment Principal Forbes
adduced as being in opposition to the theory offered by mef of
the plasticity of ice, and of the tendency of pieces of thawing ice
to unite when placed in contact.

He thought it showed that pressure was not essential to the
union of the two pieces of ice. I pointed out, in reply J, that the
film of water between the two slabs, being held up against gravity

* "On some Properties of Ice near its Melting-Point," by Prof. Forbes,
Proceedings of the Royal Society of Edinburgh, April 1858.

f Proceedings of Royal Society, May 1857, and British Association Reports, 1857.
[No. 31, supra, p. 208.]

£ Proceedings of Royal Society, Nov. 24, 1859, Vol. x. p. 159. [No. 34, supra,
p. 229.]

1861] ON PROF. FARADAY'S EXPERIMENTS ON " REGELATION " 231

by the capillary tension or contractile force of its free upper surface,
and being distended besides against the atmospheric pressure, by
the contractile force of its free surface round its whole perimeter
— except for a very small space at bottom, from which water
trickles away, or is on the point of trickling away, — exists under
a pressure which, though increasing from above downwards, is
everywhere, except at that little space near the bottom, less than
atmospheric pressure: — that hence the two slabs are urged against
one another by the excess of the external atmospheric pressure
above the internal water pressure, and are thus pressed against
one another by a force quite notable in amount ; — that, further,
the film of water existing as it does, under less than atmospheric
pressure, has its freezing point raised in virtue of the reduced
pressure ; and would therefore freeze even at the temperature of
the surrounding ice, which I took to be che freezing point for
atmospheric pressure ; and would still more strongly be impelled
to freeze by the joint action of this condition with the cold given
out in the melting by pressure of the ice at the points of contact
where the two slabs are urged against one another.

To this explanation of Principal Forbes's experiment I still
adhere as mainly correct, though admitting of some further
development and slight modification in reference to a point to
which I shall have to make further allusion in what follows, and
which seems to me to be as yet rather obscure : — the influence,
namely, of the tension in the ice due to its own weight, which
makes it not be subject internally to simple atmospheric pressure: —
and though I shall also, in what follows, point out some additional
conditions, almost necessarily present in the experiment, which,
under my general view of the plasticity of ice, would act in
conjunction with those already adduced, and would increase the
rapidity of the union.

Professor Faraday, holding it in view to remove the ground
on which my explanation of Principal Forbes's experiment was
founded, has contrived and carried out a set of new and very
beautiful experiments from which the capillary action referred to
has been completely eliminated, and he has still found the union
of the ice to occur, and to increase with time, and has met with a
curious additional phenomenon of "flexible adhesion*."

* Proceedings of Royal Society, April 26, 1860, Vol. x. p. 440. [Faraday's
Researches in Chemistry and Physics, pp. 373, 378.]

232 CONGELATION AND LIQUEFACTION [35

In these experiments, when two pieces of ice, rounded so as
to be convex at their points where mutual contact is to be
allowed, are placed in water, and are either anchored so as to be
wholly under water, or are placed floating when so formed that
they can touch one another only under water, and that, at the
water surface, there shall be a wide space between them so that
there shall be no capillary action drawing them together, he
showed that the pieces of ice, in either of these cases, if brought
gently in to contact, will adhere together; unless indeed the move-
ment bringing them into contact be so directed as to introduce
forces capable of tearing them apart again by obliquity of action,
by agitation of the water, or by other disturbances. He showed
also that, if when the two pieces of ice have become attached at
their point of contact, a slight force, such as may be given by one
or two feathers, be applied, tending to separate them, at one side
of their point of contact, they will roll round one another with a
seemingly flexible adhesion ; or that, if the point of a floating
wedge-shaped piece of ice is brought under water against the side
of another floating piece, it will stick to that piece like a leech.

He showed that if the pieces be allowed to remain for a few
moments in contact, their adhesion will become rigid, so that on
a force being applied sufficient to break through the joint, the
rupture will occur with a crackling noise, though the pieces may
still continue to hold together, rolling on one another with the
flexible adhesion. He made some other experiments nearly the
same as these, but in which he showed the flexible and rigid
adhesion to occur while there is constantly a decided tensile force
applied externally tending to pull the pieces asunder, instead of
any external force tending to press them together. He thinks
that the phenomena of flexible and rigid adhesion "under tension"
go towards showing that pressure is not necessary to "regelation."
He then gives his own idea of the flexible and rigid adhesion in
the following words: — "Two convex surfaces of ice come together;
the particles of water nearest to the place of contact, and therefore
within the efficient sphere of action of those particles of ice which
are on both sides of them, solidify ; if the condition of things be
left for a moment, that the heat evolved by the solidification may
be conducted away and dispersed, more particles will solidify,
and ultimately enough to form a fixed and rigid junction, which
will remain until a force sufficiently great to break through it is

1861] ON PROF. FARADAY'S EXPERIMENTS ON " REGELATION " 233

applied. But if the direction of the force resorted to can be
relieved by any hinge-like motion at the point of contact, then
I think that the union is broken up amongst the particles on the
opening side of the angle, whilst the particles on the closing side
come within the effectual regelation distance ; regelation ensues
there and the adhesion is maintained, though in an apparently
flexible state. The flexibility appears to me to be due to a series
of ruptures on one side of the centre of contact, and of adhesion
on the other, — the regelation, which is dependent on the vicinity
of the ice surfaces, being transferred as the place of efficient
vicinity is changed. That the substance we are considering is as
brittle as ice, does not make any difficulty to me in respect of the
flexible adhesion ; for if we suppose that the point of contact
exists only at one particle, still the angular motion at that point
must bring a second particle into contact (to suffer regelation)
before separation could occur at the first ; or if, as seems proved
by the supervention of the rigid adhesion upon the flexible state,
many particles are concerned at once, it is not possible that all
these should be broken through by a force applied on one side of the
place of adhesion, before particles on the opposite side should have
the opportunity of regelation, and so of continuing the adhesion."

The interpretation thus put by Prof. Faraday on his experi-
ments is not convincing to me ; but, on the contrary, I think the
experiments are in perfect accordance with my own theory, and
tend to its confirmation. My view of the phenomena of these
experiments is as follows : —

The first contact of the two pieces of ice cannot occur without
impact and consequent pressure ; and, small as the total force
may be, its intensity must be great, as the surface of contact
must be little more than a geometrical point. This pressure
produces union by the process of melting and regelation described
by me in previous papers. On the application of the forces from
the two feathers, at one side of the point of contact, tending to
cause separation, the isthmus of ice formed by the union of the
two pieces comes to act as a tie or fulcrum subject to tensile
force ; and consequently a corresponding pressure will occur at
the side of the isthmus, far from the feathers ; and that pressure
will effect the union of the ice at the side where it occurs.

The tensile force, it may readily be supposed, tends to preserve
the isthmus, internally at least, in the state of ice, whatever may

234 CONGELATION AND LIQUEFACTION [35

be its influence on the external molecules of the isthmus, and to
solidify such water as, having occupied pores in the interior during
previous compression, may now, by the linear tension or pull, be
reduced in cubical pressure or hydrostatic pressure, because the
melting point of wet ice is raised by diminution of pressure of
the water in contact with it*. The pull applied to the isthmus

* How the surface of a bar of ice immersed in ice-cold water, as distinguished
from the interior of the bar, may, in respect to tendency either to melt away, or to
solidify to itself additional ice from the water, be influenced by the application of
linear tension to the bar, I am not quite prepared to say positively. The applica-
tion of tension, whether linear, superficial, or cubical (that is, whether simply in
one direction, or in two directions crossing one another, or in three directions
crossing one another), to a piece of ice immersed in water at any given pressure,
atmospheric for instance, is very distinct from the application of what might be
called cubical tension, that is, diminution of hydrostatic pressure, to the surround-
ing water. In the former case the pressure of the water at the external surface of
the ice will not be reduced by the application of the tension to the ice ; though
that of the water in the internal pores may, or probably in many of them must,
be so ; but in the second case, the diminution of cubical pressure in the external
water effects the same diminution of pressure in the ice, and also in the water
occupying pores in the ice. The theory and quantitative calculation which I
originally gave (Trans. Hoy. Soc. Edin. Vol. xvi. Part 5, 1849, and Cambridge and
Dublin Math. Journ. Nov. 1850) [No. 29, supra, p. 196] of the effect of increase of
pressure in lowering the freezing point of water, and of course also of the effect of
diminution of pressure in raising it, applied solely to effects of pressure com-
municated to the ice through the water, and therefore equal in all directions, and
equally occurring in the ice and the water ; but when changes of pressure in one or
more directions are applied to the ice as distinguished from the water, the theory
does not apply in any precise way to determine the conditions of the melting of the
ice, or of its growth by the freezing of the adjacent water to its surface. There
seems to me to be yet a field open for much additional theoretical and experi-
mental investigation in this respect t ; but so far as I have applied the principle of
the lowering of the freezing point of water by pressure in developing or sketching
out a theory of the plasticity of ice, I think I have done so correctly. I perceived
that the application of pressures tending to change the form of the ice must neces-
sarily produce volume-compression in some parts of the mass, accompanied by the
occurrence of increased fluid pressure in the pores which might already exist in
those parts, or which would arise in them as a consequence of the pressure ; and
this I thought was a sufficient basis on which to rest the theory, even without
precise knowledge of all the varying influences on the melting or freezing of the
ice or water, of all the possible varieties of pressures or stresses that could be
applied to the ice, and of fluid pressure that could occur in the water con-
temporaneously with those stresses in the ice. Some additional developments
of this part of the subject, which have occurred to me, may, I hope, form the
subject of a future paper. [See No. 36, infra, p. 236.]

t [For the analytical solution of this problem, see Willard Gibbs' classical
memoir (1876) 'On the Equilibrium of Heterogeneous Substances,' reprinted in
his Collected Papers, Vol. i. pp. 185 — 218, especially the footnote, p. 197, giving
references to Prof. Thomson's work.]

1861] ON PROF. FARADAY'S EXPERIMENTS ON " REGELATION " 235

thus appears to put it out of the condition in which my theory
has clearly indicated a cause of plasticity, and I presume makes it
cease, or almost entirely cease, to be plastic.

I believe no plastic yielding of ice to tension has been dis-
covered by observation in any case, and I think there are
theoretical reasons why ice should be expected to be very brittle
in respect to tensile forces. The isthmus then being supposed
devoid of plasticity at its extended side, ultimately breaks at that
side, when the opening motion caused by the feathers has arrived
at a sufficient amount to cause fracture, and the ice newly formed
on the compressed side comes now to act as a tie instead of the
part which has undergone disruption, and holds together the two
pieces of ice, or serves as a fulcrum under tension to communicate
a compressive force to the points of the two pieces of ice im-
mediately beyond it ; and so the rolling action with a constant
union at the point of contact goes forward.

It is to be observed that the leverage of the forces applied
by the feathers is so great, compared with the distance from the
fulcrum or tensile part of the isthmus, to the compressed part in
process of formation at the other side, as that the compression
may usually be considered almost equal to the tension : arid the
tension in the extended part cannot be of small intensity, being
sufficient to break that side of the isthmus. In the experiments
which gave flexible adhesion seemingly under tension, it is not to
be admitted that tension was really the condition under which
the ice existed at the places where the union was occurring.

To apply a simple disruptive force to the whole isthmus of
ice, it would be necessary to take very special precautions in
order to arrange that the line of application of the disruptive
forces should pass through the point of contact of the two pieces.
If that were done, and the forces were gradually increased till the
cohesive strength of the isthmus were overcome, it is clear that
the two pieces of ice would separate altogether, and there would
be no flexible adhesion ; but the flexible adhesion, when it occurs,
is essentially dependent on the existence of an intense pressure
at the side of the isthmus remote from the line of the externally
applied disruptive forces, or of the single force applied in some
of the experiments to one only of the pieces, and resisted by the
inertia of the other.

It is further to be observed that tremors and slight agitations

236 CONGELATION AND LIQUEFACTION [36

to which the two pieces of ice, united at their point of contact,
may be subject, arising from undulations imparted to the water
in which the ice is immersed, by manipulation of the experimenter,
— from the tread of people on adjacent floors, — from the passage
of vehicles on neighbouring streets, — from convective movements
of the water, — and from other causes, — will be sources of power
or energy operative in bringing about an increase of adhesion
with time ; that is to say, in changing gradually the flexible into
the rigid adhesion. ,

It will now of course be obvious that the conditions involved
in the explanation just offered of Prof. Faraday's experiments
must also usually be present in the experiment of Principal
Forbes. Their incidental occurrence, however, as additional causes
increasing the rapidity of the union of the two slabs of ice, does
not overthrow the particular explanation of Principal Forbes's
experiment which I had offered as a perfect answer to the
objection raised by that experiment against my general view of
the plasticity of ice ; and as indicating clearly and certainly the
occurrence of all the conditions required for the union of the two
pieces of ice under my theory. The contingent occurrence of the
additional conditions now specially brought forward, was indeed
from the first somewhat familiar to my mind, but was left out
of the explanation as being unessential and not perhaps quite so
clearly apparent. Their occurrence has, however, now become
essential to the explanation of Prof. Faraday's new experiments: —
and by it I consider these are shown not to militate against my
general theory of the plasticity of ice, but to corroborate it strongly,
and to confirm its application to the various observed cases of the
union of two pieces of moist ice when placed in contact.

36. ON CRYSTALLIZATION AND LIQUEFACTION, AS INFLUENCED
BY STRESSES TENDING TO CHANGE OF FORM IN THE CRYSTALS.

[From the Proceedings of the Royal Society, December 5, 1861, Vol. xi. p. 473.
Also Phil Mag. Fourth Series, Vol. xxiv. (1862), pp. 395—401.]

IN a paper submitted to the Royal Society, and printed in the
Proceedings for April 25th, 1861, I directed attention in a note
[page 234] to the question of how the surface of a bar of ice in
ice-cold water, as distinguished from the interior of the bar, may,
by the application of tension to the bar, be influenced in respect
to tendency either to melt away, or to solidify to itself additional

1861] CRYSTALLIZATION AS INFLUENCED BY STRESSES 237

ice from the water ; but did not then venture to offer a positive
answer. I pointed out as a matter deserving of special attention,
and as affording scope for much additional theoretical and experi-
mental investigation, the distinction between the application to
ice in ice-cold water, of stresses tending to change its form, the
stresses not being participated in by the water; and the application
directly to the water, and through that to the ice, of cubical or
hydrostatic pressures or tensions, these being participated in by
the water and the ice alike ; and I pointed out that the theory
and quantitative calculation which I had originally given* of the
effect of pressure in lowering the freezing point of water, or of
diminution of pressure in raising it, applied solely to effects of
pressure communicated to the ice through the water, and therefore
equal in all directions, and equally occurring in the ice and the
water; but that when changes of pressure in one or more directions
are applied to the ice as distinguished from the water, the theory
does not apply in any precise way to determine the conditions of
the melting of the ice, or of its growth by the freezing of the
adjacent water to its surface; and I expressed the hope that I
might subsequently communicate to the Society some further
developments of the subject.

On following up various considerations which had then occurred
to me, I soon formed positively the opinion that any stresses
whatever, tending to change the form of a piece of ice in ice-cold
water (whether these stresses be of the nature of pressures or
tensions, that is pushes or pulls, and whether they be in one
direction alone, or in more directions than one), must impart to
the ice a tendency to melt away, and to give out its cold, which
will tend to generate, from the surrounding water, an equivalvnt^
quantity of ice free from the applied stresses. I came also to the
more general inference that stresses tending to change the form
of any crystals in the saturated solutions from which theii have
been crystallized must give them a tendency to dissolve away, and
to generate, in substitution for themselves, other crystals free

* Transactions Roy. Soc. Edin. Vol. xvi. Part 5, 1849 ; and Cambridge and
Dublin Math. Journ. Nov. 1850. [No. 29, supra, p. 196.]

f [The following note in Prof. Thomson's hand is found written in a copy
of this paper: — P.S. The quantity here not explicitly enough referred to
as an equivalent quantity is more accurately the same quantity minus that
which would be melted by the energy of the straining which disappears in the
melting.]

238 CONGELATION AND LIQUEFACTION [36

from the applied stresses or any equivalent stresses. In the
month of May last, I tested this inference by applying stresses to
crystals of common salt in water saturated with salt dissolved
from the crystals themselves ; and found the crystals to give way
gradually, with a plastic yielding, like the yielding of wet snow,
but very much slower. The crystals, with the brine in which
they were immersed, were, in the first set of experiments, placed
in a glass tube, like a test-tube, and a glass piston, or rammer,
fitting the tube loosely, so as not to be water-tight, was placed on
the top of the salt which lay like fine sand in the bottom, and the
piston was loaded with weights. The piston went on descending
from day to day through spaces, which, though small, and though
diminishing as the crystals became more compacted against one
another, were still distinctly visible. When the rate of descent
became very slow. I added more weights, and found that the rate
of descent increased, as was to be expected. I afterwards procured
a strong brass cylinder with a loosely fitted, not water-tight piston,
or rammer, and in this I subjected crystals of common salt in
their saturated brine to very heavy stresses, and thus compressed
them rapidly and easily into a hard mass like rock-salt. The top
surface presented a perfect impression of the tool marks on the
bottom of the piston, such as might have been made in wax. The
expulsion of the minute quantities of brine remaining in pores in
the salt when it has become very closely compacted, appears to be
a slow and difficult process ; as, after the pressure had been con-
tinued for about a fortnight, I still found a slight oozing of brine
from a pore which happened to exist in the side of the cylinder.

Experiments by the application of tensile stresses, or of any
other stresses than those mixed and chiefly compressive ones
which arise when the crystals are pressed in a close vessel by
a rammer, would probably not be very easily carried out ; and I
have not as yet tried any except those by pressure. I feel quite
convinced, however, that melting, or dissolving, must result from
all kinds of stresses tending to change of form. I think the
following statement may be assumed as a general physico-
mechanical principle or axiom, and I think it involves the truth
of the opinion just expressed : —

If any substance, or any system of substances, be in a condition
in which it is free to change its state (whether of molecular
arrangement, or of mechanical relative position and connexion of

1861] CRYSTALLIZATION AS INFLUENCED BY STRESSES 239

its parts, or of rest or motion), and if mechanical work be applied
to it (or put into it) as potential energy, in such a way as that the
occurrence of the change of state will make it lose (or enable it to
lose) (or be accompanied by its losing) that mechanical work from
the condition of potential energy, without receiving other potential
energy as an equivalent ; then the substance or system will pass
into the changed state. The consideration of a few cases, in some
of which there is not freedom for the substance or system to
change its state, and in others of which there is freedom, will
render the meaning of this more clear.

Gunpowder may be cited as an example of a substance in a
condition not free to change its state, although when it is made
to explode by a spark, it passes to an altered condition, and, in
doing so, even gives out a great amount of mechanical work.
That is to say, that on the whole it is more than free to change to
the exploded state, or it tends so to change, but there is some
kind of obstacle at ordinary temperatures, to the change, which
either vanishes at a high temperature, or requires the application
of mechanical work to begin the overcoming of it. When the
change is once begun, the requisite help is given to the succeeding
parts by those which have gone off first.

Again, water confined in a high reservoir is not free to go to
a lower one ; although a siphon, primarily filled with water, may
help the parts successively over the obstacle by lending to each
the requisite mechanical work in advance, which it afterwards
pays to the parts which are to follow, besides that it gives out in
its fall a great additional amount of power or energy applicable
otherwise. Two reservoirs of water, on the same level, and having
an opening between them under the water surface, would repre-
sent the case of perfect freedom for change of state ; and two on
a level with one another, but separated by a partition, would
represent the case in which no mechanical work would finally be
either given out or absorbed by the change, but in which there is
not perfect freedom to change, until a siphon or other means of
help is applied.

A bell hung from an axle and then turned up, and left resting
against a stop a little beyond its position of unstable equilibrium,
is not free to go down, but a slight pull will bring it over this
position and make it free to swing, which the work stored as
potential energy in the raising of it from its low or hanging

240 CONGELATION AND LIQUEFACTION [36

position, will cause it to do ; its fall till it comes to the bottom
being essentially accompanied by the loss of that potential energy,
as such, though not as actual energy, out of the system of which
it and the earth are the two parts, and in which change of their
distance asunder constitutes change of their potential energy.

If in an atmosphere of steam resting on water at its boiling
temperature for the pressure of the steam ; as, for instance, in the
inside of a boiler partly filled with water, and partly with steam,
an inverted cup, or bell-shaped vessel, be suspended, and if it
then, being full of steam, be forced down under the water,
mechanical work will be imparted as potential energy to the
system of which the steam and water in the boiler form one part,
and the earth is the other part ; though, for brevity of expression,
the work may be spoken of as applied to the steam and water.
In this case there is perfect freedom for the steam forced under
the water to condense and cause by communication of its latent
heat the generation of an equal quantity of steam at the surface
of the water under which the bell was sunk. The occurrence of
this change of state will enable the system to lose the potential
energy which had been imparted to it by the submersion of the
steam, or will release that energy which had been stored, and the
system will pass into the changed state', that is to say, a certain
part of the steam will change to water, and, instead of that, a
different part of the water will be changed to steam ; and this
change will be accompanied by a transmission of heat from the
part condensing to the part evaporating. This is all in accordance
with the axiom ; and we know otherwise that it must take place,
as the steam being pressed when submerged must condense and
give its latent heat to the water, and that heat must generate an
equal quantity of steam at the surface of the water, where the
pressure is less. Thus the truth of the axiom is confirmed.

If a quantity of ice and water be enclosed in a cylinder with
a water-tight piston, and if this be put into a completely closed
vessel filled with other ice and water, and if the piston then be
pulled with any given force and fixed in its new position (which
might be done in many ways, as for instance, by the use of an
axle passing air-tight through the side of the outer vessel),
mechanical work will be introduced as potential energy into the
system consisting of all the things enclosed in the outer vessel.
But there is perfect freedom for the water enclosed in the cylinder

1861] CRYSTALLIZATION AS INFLUENCED BY STRESSES 241

to proceed to freeze, obtaining the requisite cold from the ice in
the water confined around the cylinder and within the outer
vessel. The occurrence of this change would be accompanied by
the system's losing or giving up the potential energy which had
been stored in it. According to the axiom, then, the change
ought to occur. But we know otherwise that it must occur ;
because the diminution of hydrostatic pressure in the cylinder
raises the freezing point of the enclosed water, and makes it freeze
by the cold of the surrounding mixture of ice and water, which,
besides, by being itself subjected to increased pressure, tends to
give out cold by the lowering of its freezing point. Thus the
truth of the axiom is again confirmed.

Lastly, if a bar of ice in ice-cold water be subjected to any
stress (a pull for instance) tending to change its form, it will
receive mechanical work from the force, or forces, applied, and
that work will be stored as potential energy in the elasticity of
the ice. Now, if there be another piece of ice in juxtaposition
with this piece, seeing that, at the beginning, both these pieces
were free from externally applied forces, and were both in the
state in which either was perfectly free to melt and cause an
equal quantity of water to freeze to the other*, it will follow
according to the axiom, now supposed to be established, that the
application of the stress will cause this action to occur.

The case of crystals in their solutions might be stated almost
in the same words as the case of ice in ice-cold water ; but it is to

* The supposition here assumed, however, of there being perfect freedom for
either of two pieces of ice, which are immersed in the same water, and are
alike free from stresses, to melt, and, by giving out its cold, to cause an equal
quantity of water to freeze to the other, will probably not meet with assent at
present from all, as it appears to be a prevailing opinion that water and ice in
contact are not in a state of perfect indifference as to retaining or interchanging
their conditions. It is supposed that ice has a property of tending to solidify water
in contact with it, and the more so if there be ice on both sides of the water than
if on only one side. Again, it is supposed that ice is essentially colder than water
in contact with it, and that the water must continually be giving off heat to the
ice. Both these opinions are inconsistent with the supposition here assumed.
I conceive, however, that that supposition is amply confirmed by the fact that it
was involved essentially throughout the reasoning, by which I was led to conclude
that the freezing point is lowered by increase of pressure, and to calculate the
amount of the lowering. That reasoning led to true results and I believe it could not
have done so unless the supposition were true, that when water and ice are present
together their freedom to change their state on the slightest addition or abstraction
of heat, or on the slightest application of mechanical work tending to the change,
is perfect.

T. 16

242 CONGELATION AND LIQUEFACTION [36

be observed that, in their case, the necessity for the translation of
one chemical substance through another (the salt through the
dissolving liquid), and not of heat or cold alone, causes a great
slowness of the process, as compared with that of the yielding of
the ice, in ice-cold water, to applied stresses.

At an early stage of the considerations which led to the
opinions on the influence of stresses on crystallization and lique-
faction described in the present paper, the question arose to me : —
Is a spiculum or single crystal of ice, which has solidified itself in
the interior of water, and is therefore not colder than thfc water,
plastic ? Or would it, when in the water, and attached by one
end, as for instance to a crust of ice lining the containing vessel,
gradually bend upwards by its own buoyancy in the heavier water ?
My idea is that it is not plastic. I cannot conceive of the growth
of a crystal proceeding with one continuous or uninterrupted
structural arrangement, if during its growth the part already
formed undergoes permanent change of form, such as would be
due to any plastic or ductile yielding. I think we must suppose
the molecules in the interior of one crystal to be so locked into
one another, by the forces of crystalline cohesion, that any one of
them, or set of them, would experience a difficulty in making a
beginning of the change of state from solid to liquid. I have not
succeeded even in forming any clear conception of continuous
crystalline structure admitting of what may be called ductile or
malleable bending (that is, bending beyond limits of elasticity
such as occurs in lead, copper, tin, and many other metals), and
still remaining of the nature of one continuous crystal. What in
soft or malleable crystals of copper or other metals, deposited in
the electrotype process, may be the nature of the change of
molecular arrangement induced by bending them, I cannot say;
but I suppose that, in their yielding, their crystalline structure is
materially altered, and rendered discontinuous where, before, it
was continuous.

In a mass of plastic ice, I incline to think that the internal
melting, to which I attribute the plasticity, must occur at the
surfaces of junction of separate crystals or fragments of crystals ;
though probably pores, formed through melting by pressures or
stresses, may penetrate crystals by entering them from their
moistened surfaces or their junctions with other crystals. It now
becomes clear, I think, that the influence of stresses affecting the

1861] CRYSTALLIZATION AS INFLUENCED BY STRESSES 243

ice, and tending to make it melt without there being necessarily
any consequent pressure applied to the water in contact with the
ice, must come to be taken into account in any theory of the
plasticity of ice approaching to completeness.

This view does not, however, I think, supersede the theory of
the plasticity of ice sketched out by myself in former papers, but
rather constitutes an amendment, and further development of it.
Any complete theory of the plasticity of ice, and of the nature of
glacier motion, must comprise the conditions as to fluid pressure
and structural arrangement of the water and air included in the
ice, and must so explain the lamination of the glacier, seen as blue
and white veins. My brother, Professor William Thomson, in papers
in the Proceedings of the Royal Society for February [January] 25
and April 22, 1858*, endeavoured to follow up my previously
published views on the plasticity of ice with an explanation of the
laminated structure, based on the same principles. The explana-
tion he then offered, I think, cannot fail to assist in suggesting
the direction in which the true solution is ultimately to be sought
for ; yet I feel confident that no full and true solution has as yet
been found •(*.

In the foregoing part of the present paper, I have shown
reason why stresses applied to crystals when in contact with the
liquid from which they have been produced, should be expected
to cause them to melt or dissolve away. The following line of
reasoning to show that stresses applied to a crystal will cause a
resistance to the deposition of additions to it from the liquid, or,
in other words, a resistance to its growth, will, I think, prove to
be correct. When a crystal grows, the additions, it seems to me,
must lay themselves down in a state of molecular fitting, or
regular interlocking with the parts on which they apply them-
selves ; or, in other words, they must lay themselves down so as to
form one continuous crystalline structure with the parts already
crystallized. It thus seems to me that, if a crystal grows when

* [See Sir William Thomson (Lord Kelvin), Math, and Phys. Papers, Vol. v.
pp. 47 and 50.]

t I have nay brother's authority for stating that, although he believes the
physical principles suggested in his papers here referred to, to be capable of being
developed into a true explanation of the phenomena, yet he considers further
investigation necessary, and does not feel confident as to the correctness of that
part of the explanation he offered, in which the mutual action of two vesicles in a
line oblique to that of maximum pressure is considered.

16—2

244 CONGELATION AND LIQUEFACTION [36

under a stress, the new crystalline matter must deposit itself in
the same state of stress as the part is in on which it lays itself.
If, then, we consider a spiculum of ice growing in water, and if we
apply any stress, a pull for instance, to it while it is thin, and
then fix it in its distended state, and if then by the transference*
to the water beside it of cold taken from any other ice at the
freezing point we cause it to grow, which it may do if there be no
other crystal of ice beside it more free than it to receive
accessions, then the additional matter will, I think, lay itself down
in the same state of tensile stress as the original spiculum was
put into by the applied pull. The contractile force of the crystal
will thus be increased in proportion to the increase of its cross-
sectional area. If it now be allowed to contract and relax itself,
it will give out, in doing so, more mechanical work than was
applied to the original spiculum during distention. Hence there
would be a gain of mechanical work without any corresponding
expenditure; or we could theoretically have a means of perpetually
obtaining mechanical work out of nothing, unless it were the case
that greater cold is required to freeze water into ice on the
stressed crystal than on a crystal free from stress. Hence we
must suppose that a greater degree of cold will be required to
cause the stressed crystal to grow. The reasoning just given has
been for brevity stated somewhat in outline ; but I trust the full
meaning can readily be made out, and that what has been said
may suffice.

I wish now to suggest as an important subject for investigation,
The Effect of Change of Pressure (hydraulic pressure) in changing
the Crystallizing Temperatures of Saline or other Solutions of
given Strengths, — as I feel sure that such effect must exist, but
am not aware that it has been hitherto discussed or experimented
on, and as it is intimately connected with the matters under
consideration in the present paper and with subjects discussed in
previous papers, which I have submitted to the Royal Society, on
Icef.

* A theoretic air-engine for making such transferences of heat or cold was used
in the reasoning by which I determined theoretically the lowering of the freezing
point by pressure, and the same is admissible here.

t [For further developments see Willard Gibbs, loc. cit. , supra, p. 234.]

1861] INFLUENCE OF STRESS ON GROWTH OF CRYSTALS 245

37. CORRESPONDENCE WITH W. THOMSON ON THE INFLUENCE
OF STRESS ON CRYSTALLIZATION.

KILMICHAEL, BRODICK,
BY ARDROSSAN.
October 18, 1861.

MY DEAR JAMES,

I cannot quite make up my mind as to the stress, or
non stress, of new crystalline matter deposited on a crystal under
stress. I rather think there will not be stress, but a crystalline
discontinuity of some kind. Still perhaps your paper may stand
as it is. You have time enough to think of it however and it is
easy to send to Stokes either a qualifying sentence, which will
make there be nothing to recant if it should turn out that there
is not stress, or a request to cancel that part of the paper. As
far as I can see it is at least a legitimate hypothesis that there is
stress ; but I think it is also a legitimate hypothesis that there is
not stress which you reject perhaps too decidedly. I have been
thinking on writing a mathematical investigation determining the
amount of lowering of the freezing point, on the supposition that
your hypothesis holds. Your hypothesis is simply that the addition
to or subtraction from a crystal, kept elongated, is a reversible
operation. There is also a mathematical course open, to investigate
the thermal result of the work done by first elongating a crystal
and then letting it melt. I think I see how to do this perfectly
without either of the above hypotheses, but my hands are too full

just now to think of writing it out just at present.

* * * * . * * * * * *

W. THOMSON.

2 DONEGALL SQUARE WEST,
BELFAST.
October 19, 1861.

MY DEAR WILLIAM,

* * * You will see on looking over my R. S. paper
that I do state the idea rather as a probable hypothesis than
as a confidently offered theory. You will see I say that the
reasoning will "I think prove to be correct," and twice again I use
the words "it seems to me." If you still think I ought to state

246 CONGELATION AND LIQUEFACTION [37

the matter with more doubt perhaps I may do so on hearing from
you again. Still I have a pretty strong opinion that the hypo-
thesis or theory offered will turn out to be correct : and I think
the notes which I enclose to you support it pretty strongly.

I shall be very glad if when your hands are less full you can
make out the mathematical investigations as to melting and
liquefaction which you propose. I would think there would be some
data deficient such as the modulus of elasticity or the coefficient of
rigidity of the crystal of ice, salt, or other substance. * * *

JAMES THOMSON.

October 19, 1861.

NOTES ON CRYSTALLIZATION AND LIQUEFACTION.

If a crystal be subjected to stress the molecules at its surface
tend to dissolve away and the stored potential energy, making its
escape in conjunction with their dissolving, affords a power to
drive them into the fluid state even against a resistance. We may
take, as the resistance opposed, a slight reduction of temperature
in the case of a spiculum of ice in water, or of any crystal in its
saturated solution, when the solubility increases with the tem-
perature. Now as there is energy driving the molecules at the
surface into the fluid state even against a resistance, let the
diminution of temperature constituting the resistance be applied
perfectly gradually. It must at first, when infinitely small, and
afterwards while extremely small, be unable to hold in check the
force or energy tending to produce melting or dissolving of the
crystalline molecules at the surface. But that tendency must be
overcome before the process of dissolving can be reversed, and
converted into a process of deposition of new crystalline matter
from the solution, and so the lowering of temperature must be
increased to some definite amount before the reversal can take
place. The only plausible objection that I can see to this reasoning
is that perhaps it might be urged that, although to commence
the reversal of the process a real lowering of temperature (not
infinitely small) would be required ; yet that the first film of new
crystalline matter deposited might be supposed to lay itself down
free from stress and that then growth might subsequently proceed
by farther deposition on this unstressed surface. The objection
does not however seem to me to be valid.

1861] INFLUENCE OF STRESS ON GROWTH OF CRYSTALS 247

In answer to the suggested objection I would say that if its
first step held good it would merely amount to this, that a new
crop of crystals would grow over the surface of the first one from
great numbers of points where deposition might first begin, while
the spaces on the surface of the original crystal between those
points would proceed to dissolve away, and the new crop of
crystals would be undermined or cut off at their roots by this
dissolving process ; — and so no real covering of unstressed crystal-
line matter would be thrown over the stressed surface of the
original crystal. That I am justified in saying that between the
points where deposition of unstressed matter would first begin
(on the supposition that it can begin at all) the spaces on the
surface of the original crystal would proceed to dissolve away, is
evident from this ; — that on the commencement of deposition of
unstressed matter in proximity to a stressed part of the original
crystal, there would instantly be a rise of temperature to the
ordinary melting or dissolving temperature ; and the cold which
previously checked the dissolving of parts of the original crystal
exposed to the fluid and under stress would vanish by spending
itself in producing the growth of unstressed new crystals. But,
we find it to be the fact that a crystal can grow although to some
extent stressed ; for instance stressed by its own buoyancy or by
its own heaviness relatively to the surrounding fluid ; — for if its
continuous growth were interrupted by the stress, we could have
no crystals at all but only perhaps some sort of powdery or muddy
depositions of incipient crystals.

Hence on the whole I think the view I have put forward
is confirmed and is very likely to be correct; namely that
additional depositions on a stressed crystal will be likewise
stressed ; and that the stress in the original crystal will give a
resistance to the deposition of more crystalline matter in continuous

structural molecular arrangement with itself.

**********

JAMES THOMSON.

KlLMICHAEL.

October 31, 1861.

MY DEAR JAMES,

* * * I think I see some more light about deposition
on stressed surfaces but have not time to write to-night except

248 CONGELATION AND LIQUEFACTION [37

to say that, in supposing a crystal pulled artificially you do not
take into account the molecular condition of the fixtures or
appliances at the ends. It will depend on how these are dealt
with during the deposition whether the added matter is under stress
or not. But with a spiculum of ice growing vertically upwards, no

doubt the whole deposited matter will be under uniform stress.
**********

W. THOMSON.

31 WELLINGTON ROAD,

DUBLIN.
November 13, 1861.

MY DEAR WILLIAM,

* * * Now I think the action at the middle of a
crystal may be considered properly by itself, as merely dependent
on the stress in it and the temperature of the adjacent fluid ; or
its temperature and strength of solution if the crystal be not of
the same chemical composition as the fluid. Because we may
suppose such degree of cold or 'of strength of solution to be
applied at the ends or points of fixture, as will prevent any
interfering action from being propagated from the ends to the
part under consideration at the middle, so that the molecules of
fluid and crystal at the middle may be left free to act for them-
selves in the deposition of the additional matter.

One view which may illustrate my idea would be to consider
the deposition at the middle of an infinitely long crystal so that
no effect could be propagated from the ends to the part under
consideration. No doubt there will be much remaining to be
examined into both theoretically and by observation and experi-
ment. If one part in the length of a long crystal be subjected
to melting while another part is subjected to the freezing or
crystallising of additional matter to itself and if the whole be
subject to stress; there may be much to be found out as to what
will go on at the boundary between the part melting and the
part receiving accessions. I am quite at a loss to understand such
things as the transverse striae on rock crystal, and the minute facets
of geometrical forms such as triangles often visible on the nearly
plane pyramidal faces of the termination of the rock crystal.

Your affectionate brother

JAMES THOMSON.

1861] INFLUENCE OF STRESS ON GROWTH OF CRYSTALS 249

P.S. I may add that if a crystal, say of ice, were pulled
longitudinally, and if the fixtures at the ends were such as to
expose the ends to more intense stress than the middle, and if
then the cold were made such as to cause some deposition of
additional ice to occur ; I would suppose that the deposition would
occur at the middle ; although the intensely stressed parts at the
ends might be, at the same time, melting away.

GLASGOW,
November 20, 1861.

MY DEAR JAMES,

I have not had time to think with any effect about
the ice problem all this time, and therefore rather than wait
longer to reply to your last, I shall write one case for objection,
or question, with reference to your views. Suppose CD, EF to

C E

A B

be fixed ends to a vessel of water. (Imagine them perfectly rigid,
and kept at a fixed distance from one another.) Now if the
spiculum or bar of ice AB, fixed to them at its ends, be in a state
of stress, such as would be produced by initially pulling the two
ends asunder, and leaving them at an invariable distance, do you
imagine that ice deposited in the way of augmentation on AB
will all lie down in equal stress, and will therefore cause an
increasing force pulling the ends together ? I can imagine that
there would be some increase on the force pulling the ends
together, produced by the augmentation of the ice, but not that
it would go on indefinitely. I think it would be necessary to go
on applying artificially means of stretching (by clasps successively
applied for instance) to the newly deposited ice, to make it have
the same stress as the original spiculum. It seems to me most
probable that without such artificial management, the newly
deposited ice would gradually have less stress, and in fact be
gradually heterogeneous to some extent in its crystalline arrange-
ment, although not necessarily discontinuous like a distinct

A K G H

250 CONGELATION AND LIQUEFACTION [37

crystalline deposit. If A is a clamped end of a spiculum initially

pulled out longitudinally, I think

it probable that augmentations

might deposit on it somewhat

according to the dotted lines, and

that these deposits would take

off something from the stress of

the portions GH of the bar.

This would bring the end section K to bear rather more than

its original stress, because the GH portion would contract a little.

The end section K would therefore probably melt away, and

ultimately break off and relieve the whole bar from lension.

The inner and outer portions in the bar that remains would be

in states of relative constraint then of a somewhat complicated

character.

I am by no means confident that all the above is correct, but
I suggest it for your consideration. Still I cannot see that an
initial stress of two or three grains weight for instance on a fine
spiculum, could originate a powerful action tending to draw in
the sides of the vessel, and (provided these do not yield at all)
increasing without limit as the crystal grows, which I think
according to your supposition, as first stated at least, would be
the case. We were glad to have so much better accounts from
you last time. I hope the next will be still better, and will soon
come. I am getting on fairly with my work, and my leg I think
is not suffering.

Your affectionate brother,

WILLIAM THOMSON.

FROM A LETTER TO WlLLIAM THOMSON OF 29 NOV. 1861
WRITTEN BY MRS JAMES THOMSON.

James thinks when he next writes to you that he will be able
to answer satisfactorily the remarks you make (in letter of Nov. 20)
as to the growth of a crystal under stress. In the meantime he
wishes me to tell you that it is not necessary for his case to
maintain the indefinite growth in thickness of a long spiculum
when under stress. You point out that there might be a tendency
to melt away at the extremities or points of attachment of the
crystal when pulled longitudinally until at last breakage might

1861] INFLUENCE OF STRESS ON GROWTH OF CRYSTALS 251

occur at one extremity, but James says it is enough for his case
to consider what goes on at the middle of the crystal where it is
growing thicker during the time previous to the supposed breakage
and if it grows when under stress he thinks each thin lamina of
the fresh ice will form itself subject to like stress with that of
the lamina on which it lays itself down. He also thinks that he
is entitled theoretically to suppose that the cold producing the
additional freezing may be designedly so distributed as to prevent
any one part of the spiculum, whether at the end or at the middle,
from falling behind the rest in growth. That is to say, a little
extra cold applied at the parts where you suppose the crystal to
thin away would prevent it from thinning and would make it
grow equally with the rest or even more so if sufficient cold were
applied. James wishes you to observe that spicula of ice growing
as they actually do in the middle of a mass of water frozen
externally as a crust, are subject to cross strains in consequence
of their own tendency to flotation. These strains are no doubt
exceedingly small, but he thinks if a force were applied upwards
at the middle of one of them so as to bend it decidedly with an
elastic bending, the crystal might still continue to grow if sufficient
cold were supplied to the adjacent water to produce the solidi-
fication of new ice under like stress with that of the part of
the crystal on which the new ice would grow. James would not
be surprised if it should turn out that stresses in a straight
spiculum might have something to do with the origination of
branch crystals growing off from it; the branches being at the
commencement produced at points where accidentally the crystals
might grow a little quicker than at intervening points and so
being subject to less strains than those intervening points of the
original spiculum. However he does not wish to be positive on
this part of the matter.

P.S.

November 30, 1861.

MY DEAR WILLIAM,

I did not manage to get the foregoing letter ready
in time to send off to you last night. On reading it over
to-day along with your letter I think it forms my full answer
to your letter. You will see that it is of no consequence
for my case to maintain the indefinite growth of the crystal by

252 CONGELATION AND LIQUEFACTION [38

uniform laminar additions. I require only the admission that at
any moment an infinitely thin lamina added to the previous surface
will have the same stress as that previous surface has, and that
consequently to cause a crystal of ice to grow when under stress
a greater cold will be requisite than to cause one to grow when
free from stress. It will then follow as suggested in the foregoing
letter that at the most stressed points the growth will be resisted
but will be left more free at any points of the crystals of ice
which may be free from stresses. This I think may tend to cause
original straight spicula to grow out into branches
thus: — though I have not sufficiently observed
the actual growth of crystals to venture to say
much positively on this point. I am feeling better
to-day and was teaching at the College for three
hours, and out walking afterwards.

Your affectionate brother,

JAMES THOMSON.

W. Thomson replies to this in a letter of Dec. 10th, 1861, as
follows : —

"I think your last on the growth of crystals is satisfactory,
but it is a very difficult subject, and I must think more about it
before I write again on it."

38. CORRESPONDENCE WITH H. C. SORBY, F.R.S., ON
GEOLOGICAL EFFECTS OF PRESSURE.

BROOMFIELD,

SHEFFIELD.
February 5, 1862.

MY DEAR SIR,

I make no apology in doing what I should be glad
for anyone to do to me, and therefore write to you, although not
known to you personally.

I have just received the Proceedings of ike Royal Society,
and read your paper on crystallization etc. p. 473* with the greatest
pleasure; since it has been published most opportunely, and serves
most admirably to clear up a curious geological difficulty. The
fact is, I had come to very nearly the same conclusions as you
* [No. 36, supra, p. 236.]

1862] GEOLOGICAL EFFECTS OF PRESSURE 253

have, from an entirely different course of reasoning. I had made
out certain facts, and, at a meeting of our Chemical Society, had
argued that, if pressure would cause a crystal in a saturated
solution to be dissolved and crystallize again in some other part
where there was not the pressure, the whole of the difficulties
would be removed. I brought forward the subject in order to
learn if anyone had made any experiments on the subject, and
based some of my arguments on the case of ice, on which you
have written, and in relation to which you have made such
interesting discoveries. I had planned to myself the trying of
just such experiments as you suggest, but other things have
prevented my doing so.

It will perhaps be well to give you a short sketch of what I have
done, which has led me to form my conclusions ; and I should
esteem it a great favour if you will give me your opinion as to
the accuracy of my explanations.

In the Nagelflue in Switzerland are certain conglomerates of
limestone pebbles; and, when these pebbles are in contact and have
apparently been forcibly pressed against each other, one has often
made its way into the other; thus in Section, A. I have prepared

various thin sections of these pebbles to

examine with the microscope, according to
the plan described in my various published
papers, and I have thus succeeded in proving
most completely that the impressed pebble
did not yield as a plastic or as a rigid body
to the impressing pebble, but the depression has been due to the
actual removal of the limestone, and that not mechanically but
chemically. Crystalline carbonate of lime is found on the exterior
of the pebble, and in cracks where there would be no pressure ;
and, if it be correct to form the conclusion you have printed in
italics about the middle of p. 474* of your paper, i.e. if the pressure
would cause the carbonate of lime to be dissolved from the part
where one pebble pressed against the other, and to crystallize out
in another part, where free from pressure, the whole, or nearly
the whole, of the difficulties would be removed. I may say that
this question has been much studied in Germany and France,
and the best geologists there have failed to give a satisfactory
explanation of these curious impressed pebbles ; but my methods

* [See foot of p. 237.]

254 CONGELATION AND LIQUEFACTION [38

of microscopical investigation appear likely to remove all the
doubts. The only thing not entirely cleared up, if the principles
you advocate be correct, is that very often the pebble which makes
the impression has not itself been acted on ; but perhaps we may
suppose that its nature was such that its exterior resisted the
pressure in such a manner that the calcareous part was not sub-
jected to the same amount of pressure as in the case of the other,
for both are impure Limestone, and sometimes they contain a
large proportion of sand etc. It is curious that your paper should
have appeared so opportunely, for I was going to commence writing
a paper on the subject, to be published in Germany, as soon as
I had finished a few things I now have in hand ; and I aTn glad
I had not written it sooner.

Trusting that the great interest, which, as you see, I take in
the subject of your paper, will be a sufficient excuse for my thus
writing to you, and only wishing I could show you my objects
and talk the matter over with you here,

I remain, Yours very truly,

H. C. SORBY.

To H. C. SORBY, ESQ., F.R.S.

2 DONEGALL SQUARE WEST,
BELFAST.

March 14, 1862.

MY DEAR SIR,

I hope you will not attribute to any want of interest
in the subject of your letter, as to limestone pebbles having been
penetrated into by others, my having allowed so long time to
elapse with little more than a brief acknowledgment of receipt
of your letter. The phenomena you describe appear to me to be
of very great interest ; and I think it most likely that you are
right in suggesting that the theoretical views in my paper to the
R. S. on Crystallization and Liquefaction as influenced by Stresses
in the Crystals, may probably be coupled with your observed
phenomena as affording the theory of their explanation and as
confirming the supposition you had been finding yourself led to,
from quite different grounds, to the effect that pressure might
probably cause a crystal in a saturated solution to be dissolved
and to crystallize again in some other part where there was not
the pressure, since, as you argue, if this supposition were correct

1862] GEOLOGICAL EFFECTS OF PRESSURE 255

the whole of the difficulties as to your observed phenomena would
be removed.

With reference to one point which you mention, the fact
namely that "very often the pebble which makes the impression
has not itself been acted on." I think we are quite entitled to
account for this by supposing nearly as you suggest, that the two
may not be of exactly equal solubility or that the one may, from
a slight difference in chemical composition, or from some other
slight difference, be not quite so easily soluble as the other.

I shall look forward with great interest to the farther develop-
ment of the line of observation and reasoning you have entered
on in respect to this matter, and it would give me great pleasure
if opportunity should permit of my seeing your objects and
conversing with you on the subject. I think all you have
described in your letter tallies perfectly well with my views.

Believe me,

Yours very truly,

JAMES THOMSON.

BROOMFIELD,

SHEFFIELD.
March 22, 1862.
MY DEAR SIR,

You will doubtless be pleased to learn that, in the
same manner as your prediction about the thawing of ice was
proved by experiment, so also now does there appear every
probability of your prediction about the solution of salts under
pressure being established. I have been making some experi-
ments, and though they are not anything like so complete as
I intend to make them, and do not establish the feet beyond all
doubt, yet they so far clearly prove that it is uncommonly well
worth while to carry them out more thoroughly. I have experi-
mented with a solution of common salt and portions of rock salt,
since it is soluble to the same extent, or at all events sufficiently
nearly so, as not to be influenced by any small change in
temperature. I have proved that the effects of the heat of the
hand, that might influence the result, in examination and preparing
for the experiment, are not appreciable; nor was there any solution
when the crystal was exposed in the tube used for the experiment
for 24 hours. However, when in the same tube and in the same

256 CONGELATION AND LIQUEFACTION [38

concentrated solution exposed for 15 minutes to a pressure of
100 Ibs. to the square inch, then for 10 minutes to 150, and at
last for 5 minutes to 200 Ibs. per square inch, though the amount
dissolved was only small, there was no kind of doubt whatever
about it, as observed by myself and two friends who are used to
experiments.

I am going to try a much longer action, so as to be more
certain, but in the meantime thought you might like to know
that so far the result is so satisfactory.

Yours very truly,
H. C.

To Mr Sorby's letter of 22nd March, 1862, I reply on the
24th thanking him for writing : and I add : —

"As I know you have done much in investigating slaty
cleavage in rocks, I wish to suggest that it seems to me that
perhaps some interesting results in the formation of slaty cleavage
might be arrived at by pressing between two flat plates (such as
those of a screw letter copying press) Roman or Portland Cement
or some other quick or slow setting hydraulic limes when worked
with water to the pasty or clayey consistency. The screw of the
press I think should be turned at regular short intervals during
the solidification (crystallizing ?) of the stony substance of the
cement. I offer this only as a mere casual suggestion. You
may be better able to judge, than I, of the prospect of any
interesting results being obtainable in that way."

In a P.S. to same letter I add some recommendations that the
cement should be kept under water and I give this figure [omitted].

BROOMFIELD,

SHEFFIELD.
August 20, 1862.

MY DEAR SIR,

Before leaving here for the Highlands I thought
I would write a few lines to report the progress I have made in
my researches. The subject has grown famously. I have proved
beyond all doubt that when a salt occupies less space when it
dissolves it is 'more soluble, and when more space less soluble,
under pressure. I have devised a plan of keeping up a pressure

1862] CORRESPONDENCE WITH H. C. SORBY 257

of from 100 to 200 atmospheres for weeks and months together
without any trouble. So far I have not made out the law of the
increased or decreased solubility, but it varies directly as the
pressure for chloride of sodium, and I think the facts show that
it does not vary merely as the decreased space when various salts
are compared together. This is however not all, for I find that
mechanical pressure modifies chemical decomposition, and that
certain changes go on half as fast again under a pressure of
100 atmospheres. Much remains to be done, but facts seen in
studying the microscopical structure of rocks clearly show that
mechanical pressure has in some cases been the governing
principle in chemical changes, and this, combined with the
experiments hitherto made, lead me to conclude provisionally
that there is a correlation between chemical action and mechanical
forces, and that in the same way that we can get mechanical force
from chemical action, so we may also get chemical action out of
mechanical force. Will not this be a good step in advance ?
I of course look upon it with the eye of a geologist, and can
clearly perceive that it will enable us to explain in the most
simple manner a whole lot of facts which have hitherto been
nearly incomprehensible.

I hope you will be at Cambridge in October, for I shall take
a lot of my specimens with me, but shall not read a paper on the
subject.

Yours very truly,

H. C. SORBY.

[Cf. H. C. Sorby, " On the Direct Correlation of Mechanical and Chemical
Forces," Bakerian Lecture, 30 April 1863, Proc. Roy. Soc. Vol. xn. p. 538.
Also, " On Impressed Limestone Pebbles as Illustrating a New Principle in
Chemical Geology," Proc. Geological and Polytechnic Soc. of the West Riding
of Yorkshire, 22 Nov. 1865, Vol. iv. p. 458.]

39. ON THE DISINTEGRATION OF STONES EXPOSED IN BUILDINGS
AND OTHERWISE TO ATMOSPHERIC INFLUENCE.

[From the Report of the British Association, Section A : p. 35
Cambridge, 1862.]

THE author having first guarded against being understood as
meaning to assign any one single cause for the disintegration of
stones in general, gave reasons to show :

T. 17

258 CONGELATION AND LIQUEFACTION [40

1st. That there may frequently be observed cases of disinte-
gration which are not referable to a softening or weakening of the
stone by the dissolving away or the chemical alteration of portions
of itself, but in which the crumbling is to be attributed to a
disruptive force possessed by crystalline matter in solidifying
itself in pores or cavities from liquid permeating the stone.

2nd. That in the cases in question the crumbling away of
the stones, when not such as is caused by the freezing of water in
pores, usually occurs in the greatest degree at places to which, by
the joint agency of moisture and evaporation, saline substances
existing in the stones are brought and left to crystallize.

3rd. That the solidification of crystalline matter irf porous
stones, whether that be ice formed by freezing from water, or
crystals of salts formed from their solutions, usually produces
disintegration — not, as is implied in the views commonly accepted
on this subject, by expansion of the total volume of the liquid and
crystals jointly, producing a fluid pressure in the pores — but, on
the contrary, by a tendency of crystals to increase in size when in
contact with a liquid tending to deposit the same crystalline
substance in the solid state, even where, to do so, they must push
out of their way the porous walls of the cavities in which they are
contained, and even though it be from liquid permeating these
walls that they receive the materials for their increase.

40. ON GKOUND OR ANCHOR ICE AND ITS EFFECTS IN THE
ST LAWRENCE.

[Printed from MS. of paper read at Natural History and Philosophical
Society, Belfast, 7th May, 1862.]

[An abstract by myself was printed in the Whig and reissued in the
Proceedings. J. T. It was reprinted in the Philosophical Magazine,
Vol. xxiv. 1862, pp. 241—4]

IF we watch the progress of the freezing and subsequent
thawing, of a pond or lake of still water, we may find no indications
of powerful action in the ice. Everything seems dead and passive.
The stiff covering of ice forms itself and disappears without per-
haps breaking a bulrush or a blade of grass which it may have
held in its firm grasp, or disturbing perceptibly a pebble which it
may have enclosed ; and, when a few days or weeks have elapsed,

1862] GROUND OR ANCHOR ICE IN RIVERS 259

and the water has resumed its mobility, no apparent trace may
remain to indicate the previous occurrence of so different a con-
dition of the lake surface.

Often, however, in other circumstances ice manifests itself as
an agent of almost irresistible power, effecting important geological
changes, and taxing severely, and often baffling the constructive
skill of men. We see ice gathered in mountain valleys as masses
of length and breadth which may be measured in miles, and depth
in hundreds of feet ; and we find these masses grinding and
excavating the hard rocky beds over which they pass, and pro-
truding down among cultivated fields, and overwhelming bridges,
villages, or any other structures which may, too incautiously, have
been built within the limits of their possible extension. We see
icebergs swimming freely at sea, ready to crush the strongest
ships; and we find them conveying huge masses of rock, and
depositing them in the ocean at hundreds of miles distance from
their previous place.

The ice of great rivers, in climates where the winter-cold is
severe, produces striking geological effects ; and it is by far the
most formidable difficulty to be encountered in the construction of
bridges, and other engineering works, in the river channels, or
adjacent to their banks.

The ice of rivers forms itself in two very distinct modes, one as
surface ice like that formed on the surface of still water, and the
other as ice of a spongy or soft kind adhering to the bottom. The
ice formed at the bottom is designated by the various names
ground ice, anchor ice and frasil ice.

When a lake or pond of still water at any temperature above
40° F. is exposed to cold at its surface, the portions cooled are
diminished in bulk ; and, on account of the increase of their
specific gravity, they sink to the bottom, and so a circulation
is maintained until the temperature of the whole has arrived
at 40° F. the point at which water attains its maximum density.
Any farther cooling beyond that point expands the water to which
it is applied, and causes it to float. Thus the previous circulation
is brought to an end ; and the coldest stratum of water, lying at
the top, soon begins to freeze. The crust of ice when formed, and
especially when it has become thick, opposes great resistance to
the downward passage of the cold ; and the cold which, in conse-
quence of this resistance, arrives slowly at the under side of the

17—2

260 CONGELATION AND LIQUEFACTION [40

crust spends itself immediately in freezing the first water it meets
with. In this way, the deep and still water is protected from the
cold, and retains approximately the temperature of its maximum
density 40° F. ; and never freezes, nor even approaches near to the
freezing point.

Such being the conditions of the congelation of lake water, it
has long been regarded by geologists and others as a singular
circumstance that ice should ever be found growing at the bottom
of a river, and many speculations have been advanced to account
for the phenomenon. As yet, however, it would appear, none has
been put forward which has met with general acceptance as at all
satisfactory. Thus Sir Charles Lyell in a recent edition of his
Principles of Geology, after referring to the discussions on this
subject and treating of its geological bearings, leaves the origin of
the ground ice as being still an unsettled point.

From among the suggestions which at various times have been
offered, we may now set out by accepting as quite correct the view
that the essential difference between the circumstances of the
freezing of lake and river water, is that in the former case the
water is left undisturbed to the action of the cold, and is allowed
to adjust itself in strata in which the coldest parts, being also the
lightest, float to the top, — while in the rivers the whole water is,
by mixing due to its rapid flow, brought to a uniform temperature
at the freezing point from top to bottom, and is thus brought into
a condition in which it is ready to freeze at any part where addi-
tional cold may be applied.

It remains however still to be asked why is it that, in many
cases, the freezing occurs first and chiefly at the bottom, or that
the ice is found first to collect in masses there ?

To account for this it was suggested more than 30 years ago
that radiation of heat from the bottom, through the water, up to
the cold atmosphere or sky, might keep the bottom cooled so as to
effect the freezing of ice there from the water already ice cold.
Arago rejected this supposition entirely and assigned two other
reasons for the growth of the ice at the bottom. Firstly he sup-
posed that there would be a peculiar aptitude to the formation of
crystals of ice on the stones and asperities at the bottom (the
water being throughout at the freezing point), like as there is
found to be a special readiness to the formation of crystals on
rough bodies in saline solutions : — and secondly, he supposed that

1862] GROUND OR ANCHOR ICE IN RIVERS 261

the existence of less motion of the water at the bottom would
favour the growth of the crystals there. Neither of these sup-
posed reasons appears to me to be tenable now, when the principles
of crystallization are better understood than they were at the time
when this distinguished French naturalist discussed the subject : —
for, first, the water of a rapid river when freezing has abundance
of small spicula or fragments of ice floating and diffused through
it, every one of which offers at least as free a point for the recep-
tion of new ice as can be presented by asperities on the bottom : —
and secondly, the slower motion at the bottom would not favour
the occurrence of freezing of new ice there, rather than at the top.
Indeed, on the contrary, the greater fluid friction at the bottom,
and the heavier pressure there, are causes slightly tending to
oppose the freezing of new ice at the bottom.

Shortly after Arago's writings on this subject, which were
published in France in 1833, the same subject was elaborately
discussed in the Royal Society of London in a paper by the Rev.
James Farquharson*. He maintained the radiation theory, and
supposed that the ground ice grows under water much in the
same way as hoar frost does on land. His paper is certainly very
valuable as affording information from his own careful observa-
tions on the growth and appearances of the ground ice, in rivers
where he had often seen it in England.

In his description of the growth, the appearance, and the
qualities of this ice he states that when it first begins to form
on the bottoms of the streams, it presents a rudely symmetrical
appearance, which may be compared to little hearts of cauliflowers,
fixed on the bottom, having a circular outline and a protuberance
in the centre, with coral-like projections, and having a shining
silvery aspect; and that these increase in numbers and in size
until the whole bottom is covered with them. He mentions also
that this ground ice is a cavernous mass, of variously sized pieces
of ice, all small, adhering in an apparently irregular manner by
their sides, angles, or points promiscuously, and having their
interstices occupied with water.

These characters of the ground ice agree, I think, perfectly
with the view which I have to propose for its origin, and tend
to confirm that view, rather than to establish the supposition that
the ice grows like hoar frost by crystallization at the bottom.

* Phil. Trans. 1835.

262 CONGELATION AND LIQUEFACTION [40

My own view, which I may at this stage submit, is that the
crystals of ice are frozen from the water at any part of the depth
of its stream ; — whether the top, the middle, or the bottom ; where
cold may be introduced, either by contact or radiation ; and that
they may also be supplied in part by snow or otherwise ; and that
they are whirled about in currents and eddies until they come in
contact with some fixed objects to which they can adhere, and
which may perhaps be rocks or stones, or may be pieces of ice
accidentally jammed in crevices of the rocks or stones ; or may be
ground ice already grown from such a beginning.

That pieces of ice under water have the property of adhering
to one another with a continually increasing firmness, and this
even when the surrounding water is above the freezing tempera-
ture, has been shown in a set of very interesting experiments by
Professor Faraday, of which I had the pleasure of submitting my
view of the reasons to this Society in the course of last Session*.
I think too that the ready adhesion to the bottom, or to ice
already anchored there, may possibly be increased by the effects of
radiation, but I am confident that the anchor ice is not formed by
crystallization at the place where it is found adhering.

That loose crystals of ice in a river might by their union form
ground ice, is not at present quite a new suggestion ; for I find in
a Report by Mr Keefer, one of the Engineers who were engaged in
the surveys for the project of a railway bridge over the St Lawrence
at Montreal, the idea stated that snow, falling into the water, may
be converted into frasil or anchor ice. This is, I believe, correct so
far as it goes, but it is far from a full explanation, more especially
when unconnected with any experiments to show a capability in
crystals of ice to unite themselves when in contact under water ;
and it does not appear to have been generally accepted as satis-
factory by people on the spot at Montreal, where the phenomena
of the ground ice are met with on a grand scale.

The view of Mr Hodges, the Managing Engineer of the
Contractors for the great bridge since built there across the
St Lawrence, is quite different. His view is given incidentally
in a graphic description of the ice of the St Lawrence, in
his large and valuable work on the Construction of the Victoria
Bridge published since the completion of that great undertaking.
From the opportunities and necessities he met with, for observing
* [See supra, p. 231.]

1862] GROUND OR ANCHOR ICE IN RIVERS 263

and studying the ice phenomena of the St Lawrence, during the
six years or more in which he was engaged in the building of the
bridge, and in which the ice difficulties were the greatest with
which he had to contend, his description of the phenomena may
readily be accepted as valuable, and as worthy of much confidence.
It relates, not merely to the ground ice, but to the ice phenomena
in general of the St Lawrence. It describes the surface ice, and
the formidable 'shovings' which occur, when the ice is beginning to
fix itself across the surface of the river in winter, and afterwards
when it is breaking up in spring ; and it is so interesting that I
trust I may be permitted to quote it with but little abbreviation.

In submitting his description, I shall, however, have to dissent
entirely from his theoretical view of the formation of the ground
ice.

" The ice," he says, " begins to form in the St Lawrence about
the beginning of December. Then along the shores, and in the
shallow quiet places where the current is least strong, a thin ice
begins to make its appearance, gradually showing signs of increas-
ing strength and thickness. Soon after, pieces of ice begin to
come down from the lakes above ; and then, as winter advances,
anchor or ground ice comes down in vast quantities, thickening
the otherwise clear water of the river. A word as to the ' Anchor
Ice.' It appears to grow in rapid currents, and attaches itself to
the rocks forming the bed of the river, in the shape of a spongy
substance not unlike the spawn of frogs. Immense quantities
form in an inconceivably short space of time, accumulating until
the mass is several feet in depth. A very slight thaw, even that
produced by a bright sunshine at noon, disengages it, when, rising
to the surface, it passes down the river with the current. This
description of ice appears to grow only in the vicinity of rapids, or
where the water has become aerated by the rapidity of the current.
It may be that the particles or globules of cold air are whirled by
eddies until they come into contact with the rocky bed of the
river, to which they attach themselves, and being of a temperature
sufficient to produce ice, become surrounded with the serni-fluid
substance of which anchor ice is formed. ' Anchor Ice ' sometimes
accumulates at the foot of rapids in such quantities as to form a
bar across the lake (similar to bars of sand at mouths of rivers) of
some miles in extent, lifting the water in its locality several feet
above its ordinary level. This frequently happens at the foot of

264 CONGELATION AND LIQUEFACTION [40

the Cedar Rapids at the head of Lake St Louis, where a branch of
the Ottawa empties itself into the St Lawrence. Upon such occa-
sions the water at this point is dammed up to such a height as to
change its course, and run into the Ottawa, at the rate of some
four or five miles per hour. From thence it finds its way back
into the St Lawrence by the Rapids of St Anne, after performing
a circuit of some ten or twelve miles. The accumulation of ice
continues, probably for several weeks, till the river is quite full, and
so thickened as to make the current sluggish and cause a general
swelling of the waters. The pieces, too, become frozen together,
and form large masses, which by grounding, and diminishing the
sectional area of the river, cause the waters to rise still morft (there
being always the same quantity of water coming over the rapids).
Then the large masses float and move further down the river,
where, uniting with accumulations previously grounded, they offer
such an obstruction to the semi-fluid waters that the channels
become quite choked, and what is called a 'jamb' takes place.

" The surface ice, arrested in its progress, packs into all sorts
of imaginable shapes ; and, if the cold is very intense, a crust is
soon formed, and the river becomes frozen over till many square
miles extent of surface packed ice is formed. As the water rises,
the jamb against which this field rests, if not of sufficient strength
to hold it in place, gives way; when the whole river, after it is
thus frozen into one immense sheet, moves en masse down stream,
causing the 'shovings' so much dreaded by the people of Montreal.
The edges of the huge field moving irresistibly onwards, plough
into the banks of the river, in some instances to a depth of several
feet, carrying away everything within reach. In places the ice
packs to a height of 20 or 30 feet, and goes grinding and
crushing onwards till another jamb takes place, which, aided by
the grounded masses of packed ice upon the shoals and shores,
offers sufficient resistance to arrest in its progress the partially
broken up field.

" As the winter advances and the cold increases, the field of
packed ice becomes stronger, and as the lakes above become frozen
over, the ice from thence, which had hitherto tended so much to
choke the channel, ceases to come down, and the water in the river
gradually subsides, till it assumes its ordinary winter level, some
12 feet above its height in summer. The ' Ice Bridge,' i.e. the
complete and solid condition of the ice in the river, now be-

1862] GROUND OR ANCHOR ICE IN RIVERS 265

comes permanently formed for the winter, and this generally
takes place about the first or second week in January. The
thickest virgin ice seldom exceeds three feet. Upon the clear
blue waters of the St Lawrence it is perfectly transparent.

" By the middle of March, the sun becomes very powerful
at midday, which with the warm heavy rains, so affects the ice as
to make it rotten, or, as it is usually called ' honeycombed ' ; and
when it is in this state, a smart blow from any sharp-pointed
instrument will cause a block, even though three feet thick, to fall
into thousands of pieces, as if it was composed of millions of
crystallised reeds placed vertically.

" The ice when it becomes thus weakened, is easily broken up
by the winds, particularly in places where from the great depth of
water in the lakes, they do not entirely freeze over. This ice,
coming over the rapids, thickens the water, and causes a rise in
the river as in early winter. The weakened fields of ice then
begin to break up, and in a few days the river becomes free,
excepting upon the wharves and some particular parts of the
shore, where shovings may have taken place. In these places ice
may be seen for many weeks. When the lake ice comes down
before that in the river and its lower basins become rotten, great
'shovings' take place resulting in jambs, and the consequent rise
of the water level."

The anchor ice then, you will observe, from Mr Hodges's descrip-
tion, appears to grow in rapid currents and attaches itself to the
rocks forming the bed of the river in the shape of a spongy sub-
stance not unlike the spawn of frogs. Immense quantities form
in an inconceivably short space of time, accumulating till the mass
is several feet in depth. It sometimes accumulates at the foot of
rapids in such quantities as to form a bar across the river, and if
the river at the foot of the rapids enters a lake, as the St Lawrence
does a little way above Montreal, this bar comes to resemble the
bars of sand formed at the mouths of rivers ; only that the ice bar
collects and adheres together to the extent of damming up the
river for several feet above its ordinary level which the bars of
sand from want of tenacity will scarcely do.

Mr Hodges thinks that small bubbles of cold air are whirled by
the eddies till they come in contact with the rocky bed of the
river, to which they attach themselves, and then communicating
their cold to the water at the bottom which is already at the

266 CONGELATION AND LIQUEFACTION [40

freezing point, convert it into the anchor ice. With reference to
this speculation it may suffice to point out that the cold which
could be conveyed down into the water by small bubbles would be
quite inadequate to produce the results in question. The bubbles
would indeed be raised to the temperature of the surrounding
water long before reaching the bottom, and so if they were capable
of freezing any appreciable quantity of water the freezing would
occur at the top and middle rather than at the bottom.

The whole of the facts as described by various observers I
think bear out the new view which I have already offered, to the
effect that the growth of the ice at the bottom of a river is due to
the adhesion of spicula or other small pieces of ice formed else-
where by cold ; the adhesion being due to the property of ice at
the freezing point now usually designated as ' regelation,' and of
which in former papers I have stated my views at length.

P.S. I intended to say (but forgot in writing the paper) that
the rapid growth of ground ice as a bar at the foot of rapids is
much more like the accumulation there of ice formed elsewhere,
than the crystallising of new ice there.

[The following note on this paper has been kindly supplied by Prof. H. T.
Barnes, F.R.S., of Montreal* who has made extensive practical investigations
on the mode of occurrence of, and the problems presented by, Ground Ice and
Anchor Ice. An account of earlier discussions, including papers by Arago,
Elsdale, and Farquharson, has been published by Prof. Barnes in Trans. R.
S. Canada, 1906.

IT has been shown within recent years, by accurate measure-
ments of water temperatures, that a river is subject to variations
of temperature during winter months, depending on the meteoro-
logical conditions. With the advance of cold weather, and the air
temperature falling below the freezing point, the water soon
produces a quantity of ice. In the case of a lake, or river flowing
very gently — one mile per hour or less — surface ice quickly forms,
and increases in thickness as the winter progresses.

In an open river flowing too swiftly for surface ice to form, the
effect of the cold air is to produce minute crystals throughout the
mass of the river, chiefly by surface contact. These minute
crystals are carried down below the surface by the eddies in the

1862] PROF. H. T. BARNES ON GROUND ICE IN RIVERS 267

swiftly moving water. In the absence of sun, and with the action
of a cold wind or of excessive radiation at night, the temperature
of the river falls a few thousandths of a degree below the freezing
point, and during this time, the water and bodies immersed in it
become super-cooled. The flowing ice crystals under such circum-
stances readily adhere to the bottom or to objects immersed in
the water. The effect of the sun in offsetting the super-cooling of
the water is very marked ; and during the time of sunny weather
no ice is formed below the surface, no matter how cold the air
may be, and such ice as has been formed during the previous
condition of super-cooling is very rapidly melted away and
disintegrated. The action of the sun is to cause a rise in the
water temperature of the order of one-hundredth of a degree, — or
more, if there are many days of sunny weather and a long stretch
of open water. It is evident that Prof. Thomson regarded the
sticking of the ice below the surface of the water as being due to
regelation. That, however, can play no part in the phenomena ;
but the whole matter becomes simple and easy of explanation in
view of the condition of super-cooling, which has been observed
time and again in a river like the St Lawrence.

Prof. Thomson remarks that he is confident that anchor ice is
not formed by crystallization at the place where it is found
adhering. While there is a great quantity of anchor ice produced
from the sticking of the surface-formed crystals, yet there are
undoubtedly times when the nocturnal radiation is so strong
during a clear cold night that great quantities of anchor ice are
produced in situ. Both methods of growth are found in operation,
but undoubtedly the condition of super-cooling greatly accelerates
the formation. In Canada, the surface-formed crystals go by the
name of 'frazil,' and it is quite an easy matter to distinguish
true frazil from the snow which has fallen into the water during
a storm.]

268 CONGELATION AND LIQUEFACTION [41

41. ON CONDITIONS AFFORDING FREEDOM FOR SOLIDIFICATION
TO LIQUIDS WHICH TEND TO SOLIDIFICATION, BUT EXPERIENCE
A DIFFICULTY OF MAKING A BEGINNING OF THEIR CHANGE
OF STATE.

[Printed from " memoranda of Communication which I made to the Natural
History and Philosophical Society, Belfast, yesterday evening the 20th
April, 1864. I was led to make this communication at that time,
yesterday evening, though it had not been previously announced, through
the subject being touched on in my paper for the evening 'On the
Action of Frost in Disintegrating Earth and Stones*,' and because there
was time available for the Society to receive extra communications. I
had been, independently of this immediate inducement, in the intention
of giving sometime a paper on the subject. J. T. 21st April, 1864."]

I REFERRED to my taking a different view from Faraday as to
such phenomena as that water may be cooled below the freezing
point without freezing, but that the introduction of a spiculum of
ice will instantly cause solidification to set in. Faraday thought
that this is an indication that ice in contact with water has a
tendency to induce or constrain the water to assume the same
physical condition as the ice itself. I mentioned my having come
to a different or contrary opinion, that I think that when water
and ice are in contact together the freedom of each to change to
the other's state on the slightest possible cause being applied
tending to such change, is perfect f .

The new matters on this subject, which I communicated, were
in reference to the well known experiment with a strong solution
of sulphate of soda warmed in a bottle, corked, and allowed to cool,
and its solidifying then, often by the simple withdrawal of the
cork, — or if not by that, its solidification on being touched with an
iron nail or perhaps any of numerous other substances. My idea is
that some quality of the nail affords the requisite disturbance for
allowing the particles to go into the state to which they tend, but
for the commencement of the change to which a difficulty exists
which must be got over. I found that withdrawal of the cork
could not of itself be the cause ; also that the introduction of
atmospheric pressure could not be the cause, for often it did not

* [See No. 42 next page.]

t [For development of this fundamental idea see J. Willard Gibbs' great
memoir on the "Equilibrium of Heterogeneous Substances," 1876-8, reprinted
in his Scientific Papers, Vol. i. p. 320.]

1864]

ON THE CONDITIONS FOR SUPERSATURATION

269

go off; shaking the bottle would not do it; pouring to another
vessel would not do it; but I suppose there often is a partial
vacuum and that particles of dust or little crystals of sulphate
of soda are blown in. I found that I could drop in pieces, or crumbs,
of effloresced sulphate of soda from the cork without setting it
off. I therefore suppose the sulphate of soda must be in the
crystalline state to produce the effect.

I found that numerous objects such as iron nails, common pins
(brass tinned ?) etc. if wet in the warmed solution and left in it to
cool did not cause solidification, but that a dry nail afterwards
inserted did.

I found that solidification would pass through a bladder. So
the pores of a bladder do not suffice to prevent solidification in
them ; and this I mentioned as being an exception to the pheno-
menon which I had been pointing to as very usual, and exemplified
in the case of ice freezing from some kinds of moist earth in my
other paper. [See next paper.]

42. DISINTEGRATION OF EARTH BY COLUMNAR GROWTH OF ICE.
MS. Notes. 7th March 1864. After meeting of Literary Soc.

[Foundation of Paper " On the Action of Frost in Disintegrating Earth
and Stones," Belfast Nat. Hist, and Phil. Soc. 20 April 1864.]

270 CONGELATION AND LIQUEFACTION [42

Rather than freeze within the pores of the moist earthy
substance the water prefers to rise out of the moist earth, particle
by particle, and to push before it upwards the load of columnar
ice, gravel, etc. above it, and to draw up after it the water held
hanging below it through capillary tension or pull — or, in other
words, drawn up subject to less than atmospheric pressure by
negative head of from zero up to about 4 ins. or more.

Thus the remarkable phenomenon showed itself of water pass-
ing from a region of less than atmospheric pressure into a place
and condition, in the base of the columns of ice, where it was
subject to more than atmospheric pressure, being loaded with the
ice, etc., above it : — and this action went on rather than that the
water would freeze within the pores of the moist earthy bottom.

Observations on Water in Frost .Rising against Gravity rather
than Freezing in the Pores of Moist Earth.

[Partly from MS. notes for paper read at Brit. Assoc. Edinburgh, 1871 ; and
partly from abstract printed in Brit. Assoc. Volume, Part II, p. 34.]

IN this paper Professor Thomson, in continuation of a subject
which he had brought before the British Association at the
Cambridge Meeting in 1862*, on the Disintegration of stones
exposed to Atmospheric Influences, adduced some remarkable
instances which he had since carefully observed. One of these
was the case of earthy mud between paving stones in a paved
drain at Belfast. The earth was lifted up and to a great extent
detached from the paving stones, so as to present an appearance
as if the stones had been pressed down by some extraordinary load
rolled over them, or ramming with a pounder. On picking out
some pieces of the raised frozen mud, and cutting them in various
directions, Professor Thomson found, as was to be anticipated,
that they contained ice frozen in such a way as might be supposed
to result if the ice in forming itself had taken or received
additional particles from the adjacent porous mud, while these in
interposing themselves between the previously formed ice and the
adjacent porous mud had pushed that porous substance out of
their way, and if finally the mud on being deprived of a great
portion of the water by which it had previously been made very
wet had hardened by the freezing of the remaining moisture in its

* [See supra, p. 257.]

1871] DISINTEGRATION OF EARTH BY COLUMNAR GROWTH OF ICE 271

pores. The frozen mud showed the appearance of great numbers
of stratified laminae of deposition from water. These laminae were,
in many places, separated by interposed laminae of transparent
ice, which no doubt must have intruded itself molecularly and
forced open the laminar space for itself.

In another instance, observed by him in February 1864, he
showed that water from a pond in a garden had in time of frost
raised itself to heights of from four to six inches above the water
surface level of the pond by permeating the earth bank, formed of
decomposed granite, which it kept thoroughly wet, and out of the
upper surface of which it was made to ascend by the frost, so as to
freeze as columns of transparent ice. Rather than freeze within
the pores of the moist earthy substance the water prefers to rise
out of the moist earth, particle by particle ; and to push before it
upwards the load of columnar ice, gravel etc. above it, and to draw
up after it the water held hanging below it through capillary
tension or pull : or what may be called a less than atmospheric
pressure. Thus the remarkable phenomenon showed itself of
water passing from a region of less than atmospheric pressure in
the wet pores of the earth, into a place and condition in the base
of the columns of ice where it was subject to more than atmos-
pheric pressure; and to elastic stresses unequal in different
directions, from being loaded with the mass of ice and gravel above
it : and this action went on rather than that the water should
freeze within the pores of the moist earthy bottom on which the
columns stood, and which was above the water surface level of the
pond. The columns were arranged in several tiers one tier below
another*, the lower ones having been later formed than those above
them, and having pushed the older ones up. From day to day
during the frost the earth remained unfrozen, while a thick slab
of columnar ice, made up of successive tiers of columns, formed
itself by water coming up from the pond and insinuating itself
forcibly under the bases of the ice columns so as to freeze there,
pushing them up, not by hydraulic pressure, but on principles
which, while seeming not to have been noticed previously to their
having been suggested by the author at the Cambridge meeting,
appear to involve considerations of scientific interest, and to afford
scope for further experimental and theoretical researches.

* [See reproduction of author's sketch on p. 269.]

272 CONGELATION AND LIQUEFACTION [43

43. LATER INVESTIGATIONS ON THE PLASTICITY OF GLACIER ICE.

Speculations, partly new, On Plasticity of Ice and of
Hot Iron and Steel, etc.

[MS. signed J. T. llth Feb. 1888.] .

NOTWITHSTANDING the results published by Dr J. F. Main*

(Royal Soc. Proceedings May 5, 1887, pp. 329—30), and other
statements, to like effect, that ice can manifest some sort of
viscous or slow plastic yielding to stress even when decidedly
below the freezing point, I think the principle of my own
hypothesis or theory of The Plasticity of Ice published in the
Paper on Crystallisation and Liquefaction as influenced by Stresses
in the Crystal sf holds as good as ever if we merely substitute the
word Fluifaction\ for Liquefaction in the title and in the general
tenor of the paper.

It is quite as easy to imagine gaseous water substance permea-
ting between contiguous crystalline particles which are not in
continuous crystalline arrangement, as to imagine liquid water
substance permeating these interstices of discontinuity.

In iron and steel at high temperatures as in casehardening
and in cementation ? (making of blistered steel from iron bars) it
is quite certain that atoms movable, diffusible, do permeate among
parts that have crystalline characters, and that rearrangements of
crystallisation do take place. This seems closely allied to the
kinds of interpenetration imagined in my theory of Plasticity of

* [In reply to a request from Lord Bayleigh, Prof. Thomson sent the following
opinion on the paper to the Royal Society : —

"I have read the paper with great interest, I consider the Experimental
Researches to be of a very important kind : — of a kind which I have long wished
that some person would enter on and conduct with care and discrimination.

" I think it highly desirable that Dr Main's paper should be published in full in
the Proceedings"

The experimental investigation reported in Dr Main's paper was followed up by
an important memoir of date June 11, 1888, by James C. McConnel, M.A., Fellow
of Clare College, Cambridge, and Dudley A. Kidd (Roy. Soc. Proc. Vol. XLIV.
pp. 331 — 367) regarding which correspondence is printed infra.]

t [No. 36 supra, p. 236.]

J Postscript, 27th June 1889, as to nomenclature only.

Solidify, Solidification suggest Fluidify, Fluidification. Solidify and Fluidify
correspond well in form for two mutually reverse processes.

1889] PLASTICITY OF ICE AT LOW TEMPERATURES 273

Ice and other bodies exemplified in my Experiments on Plasticity
of Salt in its own brine.

Note as to Plasticity of Ice at temperatures considerably below
the Freezing Point. Date of Note is Sat. 22 June, 1889 : but the
ideas noted have been mainly or wholly devised by me long before
now in connection with my noted theory on the subject of a few
years ago : —

The movable diffusing atoms may just as well be gaseous as
liquid in the interstices between crystals of the ice. Crystals of
ice quite below the freezing point evaporate and may so give
material for condensing again somewhat as in hoar frost. Solid
camphor evaporates without passing from solid into liquid state
and thence to gaseous.

Correspondence with the late Mr J. C. McConnel, Clare College,

Cambridge.

HOTEL BUOL, DAVOS, SWITZERLAND.

May 26tk, 1889.

MY DEAR SIR,

I can hardly hope that you will have any spare copies
of papers written nearly thirty years ago, but if you have I should
be greatly obliged if you would send me one or two. The winter
before last a friend and I made some experiments on the plasticity
of ice, in which we found amongst other things that a single
crystal showed no signs of continuous yielding. Lord Rayleigh
informs me that you predicted this in a paper in the R. S. Proc.
for 1860. There is also another paper quoted by Everett (Des-
chanel, p. 313) which appeared in the R. S. Proc. for 1861 on the
Effect of Stress on Melting and Solution. I am very anxious to
read both papers. But living out here as I do, I have very seldom
the chance of referring to a good library, so it would be a great
boon to me if you could send me copies. I send you by this post
a copy of my paper.

Yours sincerely,

JAMES C. MCCONNEL.

Memo, of letter to Mr M°Connel of date llth June 1889.
...I tell him that the theory or speculation offered by me in
the Paper on Crystallization and Liquefaction as influenced by

T. 18

274 CONGELATION AND LIQUEFACTION [43

Stresses tending to change of form in the Crystals* I have ever
since believed to be true ; and that some time ago I wrote out a
statement of further extensions of that theory towards explaining
plasticity in ice at temperatures below the freezing point, and
various other cases of plasticity probably including that of red hot
and white hot iron, and the welding of iron. I say also to him : —
" Your experiments which, among other conclusions seem to show
an absence of plasticity in a continuous crystal, I regard as very
important."

J. T.

HOTEL ENDERLIN, PONTRESINA.

June 16th, 1889.

MY DEAR Sm,

Your very kind letter has been forwarded to me here
where I am staying for a short visit. I shall probably be back in
Davos within a fortnight. I am extremely obliged for your kind
offer to take so much trouble on my account and if you can let me
have printed copies of the two papers I should be very grateful.
But I can hardly ask you to have a MS. copy made. Indeed it is
probable that my doctor will allow me to make a short visit to
England — mid. August to mid. September — , and in passing
through London I can read the two papers at the British Museum
Library and copy such parts as are to me specially important. So
I beg that you will not think of going to Glasgow on my account
and that you will not spend much time in the search for the
printed copies.

I am curious to learn your explanation of the plasticity of ice
at temperatures well below the freezing point. My own views are
as follows. Since a bar of ice before and after stretching consists
of irregular crystals perfectly fitting each other, and since a single
crystal will not stretch, it is evident that there must be accommoda-
tion at the interfaces. One crystal must grow at the expense of
the next.

It remains for experiment to decide or rather discover which
crystal grows, i.e. how the motion of the molecules from crystal to
crystal depends on the direction of the optic axes and the stress.
I made an observation yesterday on this matter. In one of the
glacier grottoes I saw a projecting tongue of ice which had, as the

* [No. 36, supra, p. 236.]

1889] PLASTICITY OF ICE AT LOW TEMPERATURES 275

layers of stratification showed, originally been horizontal but had
bent down under its own weight into this position. I cut away
some pieces of ice about the point marked with a
cross, where there had been great longitudinal

pressure and long continued yielding, and took *

them into the sunshine. As usual the little discs

appeared in the ice, which lie at right angles to

the optic axis, and enabled me to see that the majority of the

crystals had their optic axes at right angles to the stress. This

suggests that under pressure the crystals whose axes are end on,

give up their material to others.

Buchanan supposes that at any temperature glacier ice contains
liquid in the shape of strong brine, which diminishes in quantity
and increases in strength as the temperature falls. But if this
lies in thin films separating the crystals, would a bar be able to
support a tension of several atmospheres ?

I am yours very truly,

JAMES C. MCCONNEL.

KNOCKDOLIAN, COLMONELL, AYRSHIRE.

September 5tk, 1889.

DEAR SIR,

Your paper on " Crystallisation and Liquefaction as in-
fluenced by Stresses Tending to Change of Form in the Crystals "
has been forwarded to me here. It was extremely kind of you to
have a manuscript copy made. On my way through London I
paid a visit to the library at the British Museum and read your
paper. But it will be most useful to me to have the full text at
hand, as it appears to me to have a most important bearing on
the plasticity of ice. I have not yet attempted to follow out the
new thoughts suggested by it ; for I am taking complete holiday,
spending a few weeks at home before starting again for another
year in Switzerland. I shall leave for Davos in about a fortnight.

I was very sorry to hear of the failure of your eyesight and
that you have been compelled to resign your Professorship. But
I hope that your eyes may, as you say, do much good service yet.
With many thanks I am

Yours very truly,

JAMES C. MCCONNEL.

18—2

CONTINUITY OF STATES IN
MATTEE

44. THE TRANSITION FROM THE LIQUID TO THE GASEOUS
STATE IN MATTER. (Unpublished notes.)

[As is well known, the idea of connecting the liquid with the gaseous
state, by a continuous inflexional curve of transition, at temperatures below
Andrews' critical point, originated with Prof. James Thomson. Very little
had been published beyond the mere suggestion until the matter was taken
up in detail in 1873 by van der Waals ; thus it has been decided to include
the following manuscript notes for historical reasons. The next stage in the
evolution of the subject is represented adequately by Clerk Maxwell's important
review of van der Waals' famous dissertation in Nature, Vol. x. Oct. 15, 1874,
pp. 477 — 480, reprinted in Maxwell's Collected Works, Vol. n. p. 407, to which
reference should be made. The models of surfaces, referred to on p. 282, as
illustrating the continuous transition for specified kinds of matter, still exist,
and have been reproduced here (p. 277). They represent the germ of the
more effective types of thermodynamic surfaces introduced by Willard Gibbs
in 1873; cf. Gibbs' Collected Works, Vol. I. pp. 1—32, 33—54, especially notes
on pp. 34, 35, and Maxwell's Theory of Heat, ed. 4, 1875, pp. 195—207.]

[THE first of the small models of the various states of carbonic
acid, as represented by points determined by volume temperature
and pressure as coordinates, here reproduced, is marked as "Model
cut out between June 6 and June 9, 1862"; the other one, with a
horn to represent the unstable region, is marked as "Cut 9th May
1869." A larger copy of the first one, made exactly to scale from
Dr Andrews' experiments, was exhibited at the South Kensington
Loan Exhibition of Scientific Apparatus in 1876. The model was
exhibited by Dr Andrews at a Royal Institution lecture in 1871 :
see his Scientific Papers, p. 340. Afterwards Clerk Maxwell went
much further by constructing to scale for carbonic acid the
Thermodynamic Surface then recently introduced by Willard
Gibbs; see his Theory of Heat, ed. 4, 1875, pp. 195—207; cf. also
a letter in Stokes' Scientific Correspondence, Vol. n. p. 34.]

1869]

MODELS OF CONTINUOUS CHANGE OF STATE

277

J

Temperatures -*-
" Model cut out between June 6 and June 9, 1862 : see MS. notes of that time."

A query (?) is marked on the model as to whether the plane face (which is a
section through the boiling-line in No. 2) should be undercut as in No. 2 into a
curved surface.

Temperatures -»•

" Cut 9th May 1869 : see also 1862 papers."
The third dimension is pressure: the critical lines are plane sections.

SOLID MODELS GIVING CURVES OF CHANGE OF STATE.

278 CONTINUITY OF STATES IN MATTER [45

45. CONSIDERATIONS ON THE ABRUPT CHANGE AT BOILING OR
CONDENSING IN REFERENCE TO THE CONTINUITY OF THE
FLUID STATE OF MATTER.

[From the Proceedings of the Royal Society , Nov. 16, 1871.]

WHEN we find a substance capable of existing in two fluid
states different in density and other properties while the temperature
and pressure are the same in both, and when we find also that an
introduction or abstraction of heat without change of temperature
or of pressure will effect the change from the one state to the
other, and also find that the change either way is perfectly
reversible, we speak of the one state as being an ordinary gaseous,
and the other as being an ordinary liquid state of the same
matter; and the ordinary transition from the one to the other we
would designate by the terms boiling or condensing, or occasionally
by other terms nearly equivalent, such as evaporation, gasification,
liquefaction from the gaseous state, etc. Cases of gasification from
liquids or of condensation from gases, when any chemical alteration
accompanies the abrupt change of density, are not among the
subjects proposed to be brought under consideration in the present
paper. In such cases I presume there would be no perfect reversi-
bility in the process ; and if so, this would of itself be a criterion
sufficing to separate them from the proper cases of boiling or
condensing at present intended to be considered. If, now, the
fluid substance in the rarer of the two states (that is, in what is
commonly called the gaseous state) be still further rarefied, by
increase of temperature or diminution of pressure, or be changed
considerably in other ways by alterations of temperature and
pressure jointly, without its receiving any abrupt collapse in
volume, it will still, in ordinary language and ordinary mode of
thought, be regarded as being in a gaseous state. Remarks of
quite a corresponding kind may be made in describing various
conditions of the fluid (as to temperature, pressure, and volume),
which would in ordinary language be regarded as belonging to the
liquid state.

Dr Andrews (Phil. Trans. 1869, p. 575) has shown that the
ordinary gaseous and ordinary liquid states are only widely sepa-
rated forms of the same condition of matter, and may be made to

1871] THE ABRUPT CHANGE AT BOILING OR CONDENSING 2*79

pass into one another by a course of continuous physical changes
presenting nowhere any interruption or breach of continuity. If
we denote geometrically all possible points of pressure and tem-
perature jointly, by points spread continuously in a plane surface,
each point in the plane being referred to two axes of rectangular
coordinates, so that one of its ordinates shall represent the
temperature and the other the pressure denoted by that point,
and if we mark all the successive boiling- or condensing-points of
temperature and pressure as a continuous line on this plane, this
line, which may be called the boiling -line, will be a separating
boundary between the regions of the plane corresponding to the
ordinary liquid state and those corresponding to the ordinary
gaseous state. But, by consideration of Dr Andrews's experimental
results, we may see that this separating boundary comes to an end
at a point of pressure and temperature which, in conformity with
his language, may be called the critical point of pressure and
temperature jointly; and we may see that, from any ordinary
liquid state to any ordinary gaseous state, the transition may be
effected gradually by an infinite variety of courses passing round
outside the extreme end of the boiling-line.

Now it will be my chief object in the present paper to state
and support a view which has occurred to me, according to which
it appears probable that, although there be a practical breach of
continuity in crossing the line of boiling-points from liquid to gas
or from gas to liquid, there may exist, in the nature of things, a
theoretical continuity across this breach having some real and
true significance. This theoretical continuity, from the ordinary
liquid state to the ordinary gaseous state, must be supposed to
be such as to have its various courses passing through conditions
of pressure, temperature, and volume in unstable equilibrium for
any fluid matter theoretically conceived as homogeneously distri-
buted while passing through the intermediate conditions. Such
courses of transition, passing through unstable conditions, must
be regarded as being impossible to be brought about throughout
entire masses of fluids dealt with in any physical operations.
Whether in an extremely thin lamina of gradual transition from a
liquid to its own gas, in which it is to be noticed the substance
would not be homogeneously distributed, conditions may exist in
a stable state having some kind of correspondence with the un-
stable conditions here theoretically conceived, will be a question

280 CONTINUITY OF STATES IN MATTER [45

suggested at the close of this paper in connexion with some allied
considerations.

It is first to be observed that the ordinary liquid state does
not necessarily cease abruptly at the line of boiling-points, as it
is well known that liquids may, with due precautions, be heated
considerably beyond the boiling temperature for the pressure to
which they are exposed. This condition is commonly manifested
in the boiling of water in a glass vessel by a lamp placed below,
when the temperature of the internal parts of the water, or, in
other words, of the parts not exposed to contact with gaseous
matter, rises considerably above the boiling-point for the pressure,
and the water boils with bumping*. At this stage it "Becomes
desirable to refer to Dr Andrews's diagram of curves showing his
principal results for carbonic acid, and to consider carefully some
of the remarkable features presented by those curves. In doing
so, we have first, in the case of the two curves for 13°*1 and 21°*5,
which pass through the boiling interruption of continuity, to guard
against being led, by the gradually bending transition from the
curve representing obviously the liquid state into the line seen
rapidly ascending towards the curve representing obviously the
gaseous state, to suppose that this curved transition is in any way
indicative of a gradual transition from the liquid towards the
gaseous state. Dr Andrews has clearly pointed out, in describing
those experimental curves, that the slight bend at about the com-
mencement of the rapid ascent from the liquid state is to be
ascribed to a trace of air unavoidably present in the carbonic acid;
and that if the carbonic acid had been absolutely pure, the ascent
from the liquid to the gaseous state would doubtless have been
quite abrupt, and would have shown itself in his diagram by
a vertical straight line, when we regard the coordinate axes for
pressure and volumes as being horizontal and vertical respectively.
Now in the diagram here submitted the continuous curves (that

* It has even been found by Dufour (Billiotlieque Universelle, Archives, year
1861, Vol. xn. " Kecherches sur 1'ebullition des Liquides ") that globules of water
floating immersed in oil, so as neither to be in contact with any solid nor with any
gaseous body, may, under atmospheric pressure, be raised to various temperatures
far above the ordinary boiling-point, and occasionally to so high a temperature as
178° 0., without boiling.

On this subject reference may also be made to the important researches of
Donny, " Sur la cohesion des Liquides et sur leur adherence aux Corps solides,"
Ann. de Chimie, year 1846, 3rd Ser. Vol. xvi. p. 167.— July 28, 1871.

1871] THE ABRUPT CHANGE AT BOILING OR CONDENSING 281

is to say, those which are not dotted) are obtained from Dr Andrews's
diagram, with the slight alteration of substituting, in accordance
with the explanations just given, an abrupt meeting instead of the
curved transition between the curve for the liquid state and the
upright line which shows the boiling stage. Looking to either
of the given curves which pass through boiling, and, for instance,
selecting the curve for 13°'l, we perceive, from what has been said
as to the conditions to which boiling by bumping is due, that for

Zero Line for VoliLmes

5|0l I I5|5| I I I6|0l I I 16(51 I I I7|0l I I I7|5I I I '8|0l I I I0|5» 1 I
Pressuures in Atmospheres

the temperature pertaining to this curve the liquid state does not
necessarily end at the boiling pressure for this temperature, and
that thus in the diagram the curve showing volumes for the liquid
state must not cease at the foot of the upright line* which marks
the boiling stage of pressure, but must extend continuously, for
some distance at least, into lower pressures in some such way as

* [The position of the upright straight line is determined by its enclosing
equal areas with the dotted curve on its two sides, as was first remarked by Max-
well in 1875 in a lecture to the Chemical Society, Nature, Vol. xi. p. 358, Collected
Papers, Vol. n. p. 425.]

282 CONTINUITY OF STATES IN MATTER [45

is shown by the dotted continuation from a to b. But now the
question arises, Does this curve necessarily end at any particular
point b ? We know that the extent of this curve in the direction
from a towards or past b, along which the liquid volume will
continue to be represented before the explosive or bumping change
to gas occurs, is very variable under different circumstances, being
much affected by the presence of other fluids, even in small
quantities, as impurities in the fluid experimented on, and by the
nature of the surface of the containing vessel, etc.

The consideration of the subject may be facilitated, and aid
towards the attainment of clear views of the mutual relations of
temperature, pressure, and volume in a given mass of a fluid may
be gained, by actually making, or by conceiving there to be made,
for carbonic acid, from the data supplied in Dr Andrews's experi-
mental results, a solid model consisting of a curved surface referred
to three axes of rectangular coordinates, and formed so that the
three coordinates of each point in the curved surface shall represent,
for any given mass of carbonic acid, a temperature, a pressure, and
a volume which can coexist in that mass. It is to be noticed here
that in his diagram of curves the results for each of the several
temperatures experimented on are combined in the form of a
plane curved line referred to two axes of rectangular coordinates,
one of each pair of ordinates representing a pressure, and the
other representing the volume corresponding to that pressure at
the temperature to which the curve belongs. Now to form a
model such as I am here recommending, and have myself made,
Dr Andrews's curved lines are to be placed with their planes
parallel to one another, and separated by intervals proportional to
the differences of the temperatures to which the curves severally
belong, and with the origins of coordinates of the curves situated
in a straight line perpendicular to their planes, and with the axes
of coordinates of all of them parallel in pairs to one another, and
then the curved surface is to be formed so as to pass through
those curved lines smoothly or evenly*. The curved surface so
obtained exhibits in a very obvious way the remarkable phenomena

* For the practical execution of this, it is well to commence with a rectangular
block of wood, and then carefully to pare it down, applying, from time to time, the
various curves as templets to it, and proceeding according to the general methods
followed in a shipbuilder's modelling-room in cutting out small models of ships
according to curves laid down on paper as cross sections of the required model at
various places in its length.

1871] THE ABRUPT CHANGE AT BOILING OR CONDENSING 283

of the voluminal conditions at and near the critical point of
temperature and pressure, in comparison with the voluminal
conditions throughout other parts of the range of gradually varying
temperatures and pressures to which it extends, and even through-
out a far wider range into which it can in imagination be conceived
to be extended. It helps to afford a clear view of the nature and
meaning of the continuity of the liquid and gaseous states of
matter. It does so by its own obvious continuity throughout its
expanse round the end of the range of points of pressure and
temperature where an abrupt change of volume can occur by
boiling or condensing. On the curved surface in the model
Dr Andrews's curves for the temperatures 13°'l, 210-5, 31°'l,
32°'5, 350>5, and 48°'l Centigrade, which afford the data for its
construction, may with advantage be all shown drawn in their
proper places. The model admits of easily exhibiting in due
relation to one another a second set of curves, in which each would
be for a constant pressure, and in each of which the coordinates
would represent temperatures and corresponding volumes. It
may be used in various ways for affording quantitative relations
interpolated among those more immediately given by the
experiments.

We may now, aided by the conception of this model, return
to the consideration of continuity or discontinuity in the curves
in crossing the boiling stage. Let us suppose an indefinite
number of curves, each for one constant temperature, to be drawn
on the model, the several temperatures differing in succession by
very small intervals, and the curves consequently being sections
of the curved surface by numerous planes closely spaced parallel
to one another and to the plane containing the pair of coordinate
axes for pressure and volume. Now we can see that, as we pass
from curve to curve in approaching towards the critical point from
the higher temperatures, the tangent to the curve at the steepest
point or point of inflection is rotating, so that its inclination to
the plane of the coordinate axes for pressure and temperature,
which we may regard as horizontal, increases till, at the critical
point, it becomes a right angle. Then it appears very natural to
suppose that, in proceeding onwards past the critical point to
curves successively for lower and lower' temperatures, the tangent
at the point of inflection would continue its rotation, and the
angle of its inclination, which before was acute, would now become

284 CONTINUITY OF STATES IN MATTER [45

obtuse. It seems much more natural to make such a supposition
as this than to suppose that in passing the critical point from
higher into lower temperatures the curved line, or the curved
surface to which it belongs, should break itself asunder, and should
come to have a part of its conceivable continuous course absolutely
deficient. It thus seems natural to suppose that in some sense
there is continuity in each of the successive curves by courses
such as those drawn in the accompanying diagram as dotted curves
uniting continuously the curves for the ordinary gaseous state with
those for the ordinary liquid state.

The physical conditions corresponding to the extension of the
curve from a to some point b we have seen are perfectly attainable
in practice. Some extension of the gaseous curve into points of
temperature and pressure below what I have called the boiling-
or condensing-line (as, for instance, some extension such as from c
to d in the figure) I think we need not despair of practically
realizing in physical operations. As a likely mode in which to
bring steam continuing gaseous to points of pressure and tem-
perature at which it would collapse to liquid water if it had any
particle of liquid water present along with it, or if other circum-
stances were present capable of affording some apparently requisite
conditions for enabling it to make a beginning of the change of
state*, I would suggest the admitting speedily of dry steam
nearly at its condensing temperature for its pressure (or, to use a
common expression, nearly saturated) into a vessel with a piston
or plunger, all kept hotter than the steam, and then allowing the
steam to expand till by its expansion it would be cooled below
its condensing-point for its pressure; and yet I would suppose
that if this were done with very careful precautions the steam
might not condense, on account of the cooled steam being surrounded
entirely with a thin film of superheated steam close to the superheated

* The principle that "the particles of a substance when existing all in one
state only, and in continuous contact with one another, or in contact only under
special circumstances with other substances, experience a difficulty of making a
beginning of their change of state, whether from liquid to solid, or from liquid to
gaseous, or probably also from solid to liquid," was proposed by me, and, so far as
I am aware, was first announced in a paper by me in the Proceedings of the Royal
Society for November 24, 1859 (Vol. x. p. 158) [see supra, p. 228], and in a paper
submitted to the British Association in the same year.

In the present paper, at the place to which this note is annexed, I adduce the
like further supposition that a difficulty of making a beginning of change of state
from gaseous to liquid may also probably exist.

1871] THE ABRUPT CHANGE AT BOILING OR CONDENSING 285

containing vessel. The fact of its not condensing might perhaps
best be ascertained by observations on its volume and pressure.
Such an experiment as that sketched out here would not be
easily made, and unless it were conducted with very great pre-
cautions, there could be no reasonable expectation of success in
its attempt ; and perhaps it might not be possible so completely
to avoid the presence of dust or other dense particles in the steam
as to make it prove successful. I mention it, however, as appearing
to be founded on correct principles, and as tending to suggest
desirable courses for experimental researches. The overhanging
part of the curve from e to f seems to represent a state in which
there would be some kind of unstable equilibrium ; and so,
although the curve there appears to have some important theoretical
significance, yet the states represented by its various points would
be unattainable throughout any ordinary mass of the fluid. It
seems to represent conditions of coexistent temperature, pressure,
and volume in which, if all parts of a mass of fluid were placed,
it would be in equilibrium, but out of which it would be led to
rush, partly into the rarer state of gas, and partly into the denser
state of liquid, by the slightest inequality of temperature or of
density in any part relatively to other parts. I might proceed to
state, in support of these views, several considerations founded on
the ordinary statical theory of capillary or superficial phenomena
of liquids, which is dependent on the supposition of an attraction
acting very intensely for very small distances, and causing intense
pressure in liquids over and above the pressure applied by the
containing vessel and measurable by any pressure-gauge. That
statical theory has fitted remarkably well to many observed
phenomena, and has sometimes even led to the forecasting of new
results in advance of experiment. Hence, although dynamic or
kinetic theories of the constitution and pressure of fluids now
seem likely to supersede any statical theory, yet phenomena may
still be discussed according to the principles of the statical theory;
and there may be considerable likelihood that conditions
explained or rendered probable under the statical theory would
have some corresponding explanation or confirmation under any
true theory by which the statical might come to be superseded.
With a view to brevity, however, and to the avoidance of putting
forward speculations perhaps partly rash, though, I think, not
devoid of real significance, I shall not at present enter on details

286 CONTINUITY OF STATES IN MATTER [46

of these considerations, but shall leave them with merely the
slight suggestion now offered, and with the suggestion mentioned
in an earlier part of the present paper, of the question whether
in an extremely thin lamina of gradual transition from a liquid
to its own gas, at their visible face of demarcation, conditions may
not exist in a stable state having a correspondence with the un-
stable conditions here theoretically conceived.

46. SPECULATIONS ON THE CONTINUITY OF THE FLUID STATE
OF MATTER, AND ON RELATIONS BETWEEN THE GASEOUS, THE
LIQUID, AND THE SOLID STATES.

[From the Report of the British Association, Edinburgh, Section A,
1871, p. 30.]

THROUGH the recent discovery of Dr Andrews on the relations
between different states of fluid matter, a difficulty in the applica-
tion of our old ordinary language has arisen. He has shown the
existence of continuity between what is ordinarily called the liquid
state and what is ordinarily called the gaseous state of matter.
He has shown that the ordinary gaseous and ordinary liquid states
are only widely separated forms of the same condition of matter,
and may be made to pass into one another by a course of continuous
physical changes presenting nowhere any interruption or breach
of continuity. If, now, there be no distinction between the liquid
and gaseous states, is there any meaning still to be attributed to
those two old names, or ought they to be abandoned, and the
single name the fluid state to be substituted for them both ? The
answer must be that in speaking of the whole continuous state we
have now to call it simply the fluid state ; but that there are two
regions or parts of it, meeting one another sharply in one way,
and merging gradually into one another in a different way, to
which the names liquid and gas are still to be applied. We can
have a substance existing in two fluid states different in density
and other properties, while the temperature and pressure are the
same. in both: and we may then find that an introduction or
abstraction of heat without change of temperature or of pressure
will effect the change from the one state to the other, and that
the change either way is perfectly reversible. When we thus

1871] THE TRIPLE POINT 287

have two different states present together in contact with one
another, we have a perfectly obvious distinction, and we can
properly continue to call one of them a liquid state and the other
a gaseous state of the same matter. The same two names may
also reasonably be applied to regions or parts of the fluid state
extending away on both sides of the sharp or definite boundary,
wherever the merging of the one into the other is little or not at
all apparent. If we denote geometrically all possible points of
temperature and pressure jointly, by points spread continuously in
a plane surface, each point in the plane being referred to two axes
of rectangular coordinates, so that one of its ordinates shall repre-
sent the pressure and the other the temperature denoted by that
point, and if we mark all the successive boiling- or condensing-
points of pressure and temperature as a continuous line on this
plane, this line, which may be called the boiling-line, will be a
separating boundary between the regions of the plane correspond-
ing to the ordinary liquid state and those corresponding to the
ordinary gaseous state. But by consideration of Dr Andrews's
experimental results (Phil. Trans. 1869), we may see that this
separating boundary comes to an end at a point of temperature
and pressure which, in conformity with his language, may be
called the critical point of pressure and temperature jointly ; and
we may see that from any ordinary liquid state to any ordinary
gaseous state the transition may be gradually effected by an
infinite variety of courses passing round the extreme end of the
boiling-line.

Fig. 1 is a diagram to illustrate these considerations and some
allied considerations to which they lead in reference to transitions
between the three states, the gaseous, the liquid, and the solid.
This figure is intended only as a sketch to illustrate principles,
and is not drawn according to measurements for any particular
substance, though the main features of the curves shown in It are
meant to relate in a general way to the substance of water, steam,
and ice. A X and A Y are the axes of coordinates for pressures
and temperatures respectively; A, the origin, being taken as the
zero for pressures and as the zero for temperatures on the Centi-
grade scale. The curve L represents the boiling-line. This
terminates towards one direction in the critical point E ; it passes
in the other direction to T, the point of pressure and temperature
where solidification sets in. This point T is to be noticed as a

288

CONTINUITY OF STATES IN MATTER

[46

remarkable point of pressure and temperature, as being the point
at which alone the substance, pure from admixture with other
substances, can exist in three states, solid, liquid, and gaseous,
together in contact with one another. In making this statement,
however, the author wishes to submit it subject to some reserve
in respect to conditions not as yet known with perfect certainty.
He observes that we might not be quite safe in assuming that the
melting point of ice solidified from the gaseous state is the same
as the melting point of ice frozen from the liquid state, and in
making other suppositions, such as that the same quantity of heat
would become latent in the melting of equal quantities of ice
formed in these two ways. Such considerations as these into
which we are forced if we attempt to sketch out the course of the

Fig. i.<

boiling-line, and to examine along with it the corresponding
boundary-lines between liquid and solid and between gas and
solid, may be useful in suggesting questions for experimental and
theoretical investigation which may have been generally overlooked
before. Proceeding, however, upon assumptions such as usually
are tacitly made, of identity in the thermal and dynamic conditions
of pure ice solidified in different ways, the author points out that
we must suppose the three curves (namely, the line between gas

1871] THE TRIPLE POINT 289

and liquid, the line between liquid and solid, and the line between
gas and solid) to meet in one point, shown at T in the figure.
This point of pressure and temperature for any substance may
then be called the triple point for that substance. In the figure
the line TM represents the line between liquid and solid. It is
drawn showing in an exaggerated degree the lowering of the
freezing temperature of water by pressure, the exaggeration being
necessary in order to allow small changes of temperature to be
perceptible in the diagram. The line TN represents the line
between the gaseous and the solid states of water substance. The
two curves TL and TN, one between gas and liquid and the other
between gas and solid, have been constructed for water substance
through a great range of temperatures and pressures by Regnault,
from his experiments on the pressure of saturated aqueous gas at
various temperatures above and below 0° Centigrade*. He has
represented and discussed his results above and below the tem-
perature at which the water freezes (which in strictness is not
0° C., but is the freezing temperature of water in contact with no
atmosphere except its own gas), as if one continuous curve could
extend for both. As brought out experimentally, indeed, they
present so little appearance of any discontinuity that the distinct-
ness of the two curves from one another might readily escape
notice in the consideration of the experimental results. Prof.
Thomson points out, however, that the range from temperatures
below to temperatures above freezing comprises what ought to be
regarded as two essentially distinct curves meeting one another in
the point T] and he further suggests that continuations of these
curves, sketched in as dotted lines TP and TQ, may have some
theoretical or practical significance not yet fully disco veredf. He
thinks it likely that out of the three curves at least the one, MT,
between liquid and solid may have a practically attainable exten-
sion past T, as shown by the dotted continuation TR. Various
known experiments seem to render this supposition tenable,
whether the condition supposed may have been actually realized
in experiments hitherto or not. He thinks, too, that there is
much reason to suppose that the curve LT between gas and liquid
has a practically attainable extension past T, as shown by the
dotted continuation TP.

* Memoir es de VAcademie des Sciences, 1847, pi. viii.
t [Of. infra, p. 298.]
T. 19

290 CONTINUITY OF STATES IN MATTER [46

In reference to the continuity of the liquid and gaseous states,
Prof. Thomson showed a model in which Dr Andrews's curves for
carbonic acid are combined in a curved surface, obtained from
them, which is referred to three axes of rectangular coordinates,
and is formed so that the three coordinates of each point in the
curved surface shall represent, for any given mass of carbonic acid,
a pressure, a temperature, and a volume, which can coexist in that
mass. This curved surface shows in a clear light the abrupt change
or breach of continuity at boiling or condensing, and the gradual
transition round the extreme end of the boiling-line. Using this
model and a diagram of curves represented here in fig. 2 [supra,
p. 281], the author explained a view which had occurred \o him,
according to which it appears probable that although there be a
practical breach of continuity in crossing the line of boiling-points
from liquid to gas, or from gas to liquid, there may exist, in the
nature of things, a theoretical continuity across this breach, having
some real and true significance. The general character of this
view may readily be seen by a glance at fig. 2 [supra, p. 281] in
which Dr Andrews's curves are shown by continuous lines (not
dotted), and curved reflex junctions are shown by dotted lines
connecting those of Dr Andrews's curves which are abruptly
interrupted at their boiling- or condensing-points of pressure. It
is to be understood that each curve relates to one constant tem-
perature, and that pressures are represented by the horizontal
ordinates, and corresponding volumes of one mass of carbonic acid
constant throughout all the curves are represented by the vertical
ordinates. The author points out that, by experiments of Donny,
Dufour, and others*, we have already proof that a continuation of
the curve for the liquid state past the boiling stage for some
distance, as shown dotted in fig. 2, from a to some point b towards
/, would correspond to states already attained. He thinks we
need not despair of practically realizing the physical conditions
corresponding to some extension of the gaseous curve such as from
c to d in the figure. The overhanging part of the curve from e to
f he thinks may represent a state in which there would be some
kind of unstable equilibrium; and so, although the curve there
appears to have some important theoretical significance, yet the
states represented by its various points would be unattainable

* Donny, Ann. de Chimie, 1846, 3rd series, Vol. xvi. p. 167 ; Dufour, Biblio-
theque Universelle, Archives, 1861, Vol. xn.

1871] THE TRANSITIONS BETWEEN DIFFERENT STATES 291

throughout any ordinary mass of the fluid. It seems to represent
conditions of coexistent temperature, pressure, and volume, in
which, if all parts of a mass of fluid were placed, it would be in
equilibrium, but out of which it would be led to rush, partly into
the rarer state of gas, and partly into the denser state of liquid, by
the slightest inequality of temperature or of density in any part
relatively to other parts.

47. SPECULATIONS ON THE CONTINUITY OF THE FLUID STATE OF
MATTER, AND ON TRANSITIONS BETWEEN THE GASEOUS, THE
LIQUID, AND THE SOLID STATES.

[From the Proceedings of the Belfast Natural History and Philosophical
Society, November 29, 1871.]

THE author commenced by referring to two recent communi-
cations made by him to the Royal Society of London* and the
British Association f, in which he had advanced some new views
as to relations among the states of matter commonly named,
distinctively, the Gaseous, the Liquid, and the Solid states. The
paper, of which an abstract is given here, was arranged for the
purpose of submitting to this society an account of the chief new
views comprised in those two previous papers, together with such
additional explanations and illustrations as might tend to render
the subject generally intelligible ; and farther, in this new paper
some later theoretical considerations, constituting an additional
development of one part of the subject, were, for the first time,
brought forward J.

The question may be asked at the outset, What is to be under-
stood by the three states — the Gaseous, the Liquid, and the Solid?
These names are familiar to all of us, and we are all accustomed
to associate each with some idea, more or less definite, of a
character or condition of matter. We have all been long accus-

* Royal Society Proceedings, No. 130, 1871 [supra, p. 278].

t British Association Transactions, Edinburgh Meeting 1871, p. 30 [supra,
p. 286].

£ See p. 32, where there are introduced considerations showing the way in
which the curves between gas and liquid, and between gas and solid, must cross
one another. [These are here omitted for brevity. They are further developed in
Paper No. 48 infra, p. 297.]

19—2

292 CONTINUITY OF STATES IN MATTER [47

tomed to conceive of matter as existing in one or other of three
states spoken of as the gaseous, the liquid, and the solid states.
The transition from each of these to any other has usually been
regarded as abrupt ; or at least this may be said, if we except the
as yet imperfectly understood phenomena of gradual hardening of
some substances such as melted glass, or melted pure iron. We
have been accustomed to notice, as among the usual properties of
liquids kept at any of various temperatures, their powerfully
resisting compression, and gradually, but very slightly, expanding
on the diminution of the pressure to which they are exposed, till
they attain a certain volume dependent on their temperature,
beyond which volume they will not admit of farther ^gradual
expansion with gradual diminution of pressure, but at which, with
no change of pressure, an abrupt augmentation of volume super-
venes, accompanied by the sudden attainment of a greatly altered
set of characters and properties commonly recognised as specially
pertaining to the gaseous state of matter. Among these altered
properties, one of the most remarkable is that of unlimited farther
gradual expansibility by farther gradual reduction of pressure.
The abrupt change of volume and of other properties thus noticed,
has ordinarily been understood as an absolute and complete
separation between all liquid states and all gaseous states of the
same matter. It is now found, however, that this distinction is
incomplete ; and that it is insufficient to separate any one state,
or set of states, from any other state or set of states ; or to form
a separation or distinction between what in common language
are called liquids, and what in common language are called gases.
If we consider water and steam present together in mutual
contact in a boiler or in a glass flask heated by a flame or otherwise,
we observe a very decided distinction between the liquid water,
and the -steam, or gaseous water-substance, enclosed together in
the vessel. The two are identical in substance, they have both
the same pressure (one atmosphere if the vessel is open), and they
have both the same temperature (100° Centigrade; the ordinary
boiling temperature, if the vessel is open). Yet while both of
them are alike in substance, and in pressure, and in temperature,
they are very different in density, or in volume for a given mass ;
and very different too in respect to their possession of latent
heat. Here we have a sharp definite distinction of two states
with a perfectly abrupt change from the one to the other, called

1871] THE TRANSITIONS BETWEEN DIFFERENT STATES 293

evaporation or condensation, which is effected without any change
whatever of either pressure or temperature.

Having here a perfectly abrupt distinction, we can properly
speak of the two states under different names, liquid and gaseous.

But now, to view the matter otherwise, let us commence with
this liquid water and steam in mutual contact ; and, whatever be
their existing temperature and consequent pressure, density, and
latent heat, let us for distinction call the existing condition of
each its original condition; and let us take some of the liquid
water away from the steam, and treat it separately. We can cool
this water, and so bring it to a new condition. We can then at
pleasure either relieve it from so much pressure, or we can
compress it more ; and in either case we effect another alteration
of its state or condition. When we have it under more than its
original pressure, we can heat it to more than its original
temperature, and thus we bring it into yet another new condition
or state. We can make as many such changes as we please, in
varied ways, without meeting any abrupt change at all; or without
finding any change sufficient to lead us to suspect any important
alteration to have occurred requiring a new name for a new state.
We only say that the liquid water has been cooled or compressed,
or relieved of pressure, or compressed and warmed, or otherwise
changed, by separate or combined changes of temperature and
pressure ; but we consider the fluid dealt with as being still liquid
water in continuously variable conditions. The steam, too, which
was originally in contact with the water; and so had the same
temperature and pressure as the water had ; is, if taken away from
the water and treated separately, capable of undergoing gradually
varied changes of state or condition quite corresponding to those
already described which the liquid water is capable of undergoing.
Thus, for instance, the steam or gaseous water-substance may
without any sudden or abrupt change be raised in temperature, or
lowered in pressure, or altered in both these ways conjointly, or it
may be raised in temperature and raised in pressure also ; and,
from each state so attained to every other, transitions may be
effected in an infinite variety of perfectly gradual ways. Thus we
have seen (1st), that between water and steam in contact with
one another, there is an abrupt transition ; (2nd), that the water-
substance, taken initially in its liquid condition when in contact
with the steam, admits of receiving an infinite variety of perfectly

294 CONTINUITY OF STATES IN MATTER [47

gradual changes of state ; (3rd), that the water-substance, taken
initially in its gaseous condition when in contact with the liquid
water, admits of receiving an infinite variety of perfectly gradual
changes of state. Now, farther, through the researches and
discoveries of Dr Andrews in recent years, we are led to conclude
that these varied states of the water, and varied states of the
steam, in their wide divergence from the initial conditions of the
water and steam in mutual contact ; which were alike with one
another in pressure and temperature, but quite distinct in other
respects; come to meet again: and in coming to this new meeting,
very different from their previous abrupt meeting, they merge
perfectly gradually into one another. He has shown by experi-
ments on carbonic acid and several other substances, that the
ordinary gaseous and the ordinary liquid states are only widely
separated forms of the same condition of matter, and may be made
to pass into one another by a course of continuous physical changes
presenting nowhere any interruption or breach of continuity.

These experiments of Dr Andrews are to be found described in
detail in his original memoir in the Transactions of the Royal
Society for 1869, and they have been explained by himself to the
Belfast Natural History and Philosophical Society. The carbonic
acid or other fluid experimented on was confined in the upper
part of a small glass tube, hermetically sealed at the upper end,
the cavity for containing the fluid being made variable in capacity
at pleasure by an arrangement for forcing in a mercurial column
from below more or less by means of a hand screw. He made
experiments on the effects of changes of pressure and of tempera-
ture on various fluids; but carbonic acid was the one which he
selected for his most extensive and elaborate experiments. He
had means provided for making observations on the co-existing
pressures, temperatures, and volumes of the carbonic acid in
successive experiments, with all requisite accuracy for the esta-
blishment of very remarkable conclusions. In this apparatus,
when gaseous carbonic acid commencing with a light pressure is
enclosed and maintained at any ordinary temperature of the
atmosphere, at, for instance, 10° Centigrade or 50° Fahr., it shows
liquefaction on being compressed. The liquid carbonic acid may
be seen lying in the bottom of the cavity with gaseous carbonic
acid above it, there being a visible surface of demarcation between
the two.

1871] THE TRANSITIONS BETWEEN DIFFERENT STATES 295

But, otherwise, if this same carbonic acid, still enclosed in the
cavity, be taken at first at 10° "Centigrade as before, and at any
pressure which allows it to remain gaseous, and if it be warmed to
any temperature above 31° Cent, (that is to say, above 88° Fahr.),
it may, at this higher temperature, be subjected to any pressure,
however great, without showing any liquefaction. While subject
to heavy pressure, it may be cooled to its original temperature of
10° Cent., and yet no appearance of liquefaction will have set in,
though it be now in a state even more dense than when it was in
the previous example compressed at 10° to the liquid state from
the gaseous. It may now, while maintained at 10° Cent., be
relieved of pressure, till at last it will begin to boil; thereby
showing that it is now liquid and must have really passed from
the gaseous to the liquid state, through elevated temperatures and
pressures, by a series of gradual changes presenting nowhere any
interruption or breach of continuity. Through this abrupt process
of boiling, it reverts to the gaseous state ; yet it has nowhere
passed through the contrary abrupt process of condensing. Again,
the reverse of this entire cycle of operations may be effected. We
may this time commence at 10° Centigrade, with the cavity
containing gaseous carbonic acid at top, and liquid carbonic acid
below. Compress so as to diminish the volume, and condensation
from gas to liquid will set in, and with continued diminution of
volume will go on, without any change of temperature or pressure,
till no part remains gaseous. Retaining the same temperature of
10°, press more heavily and then raise the temperature. Thus
the critical temperature of 31° Cent, may be surpassed without
boiling setting in. Now enlarge the cavity maintaining any
temperature above 31° Cent., and the confined fluid, which we
may have hitherto regarded as liquid, enlarges with the cavity
and abates in pressure without boiling or showing any appearance
of evaporation. Continue this process till the pressure in abating
reverts to its original amount. We may now lower the tempera-
ture, retaining this regained original pressure, and on arriving at
10° Cent., while diminishing the volume, we shall find the fluid
beginning to show liquefaction setting in, so that we may be sure
it is now gaseous. Thus we have had a gradual transition from
the liquid state to the gaseous state made manifest without
any abrupt change such as that of boiling or evaporation having
occurred.

296 CONTINUITY OF STATES IN MATTER [47

We may next consider a series of changes during which gaseous
and liquid carbonic acid are kept constantly present together in
the cavity. Suppose that we commence at an ordinary atmospheric
temperature of 10° Centigrade, and that we have already com-
pressed gaseous carbonic acid till a portion of it has condensed to
the liquid state. We are now to proceed by raising the temperature
and raising the pressure so as to keep the fluid continually
partly liquid and partly gaseous ; and so we are to keep continually
passing through a succession of boiling or condensing points of
pressure and temperature jointly. To do this we may proceed
thus : —

(1) Maintaining the volume constant, heat the heterogeneous
fluid, but not so much as to evaporate the whole. This causes a
part of the liquid to evaporate, and expands the remainder in
spite of the increased pressure of the gas above. This makes the
remaining liquid less dense and the gas more dense than before ;
and so the two have approached nearer to one another in density.

(2) Keeping temperature constant, diminish the cavity,
compressing its contents so as to condense to the liquid state what
had evaporated in the previous process. This does not alter the
pressure, but leaves the original quantities in the liquid and
gaseous states, and nearer to one another in density than at first.
Go on in the same way by heating and compressing and taking
care so to modulate the two processes as to maintain always a
portion of the fluid gaseous and a portion liquid. The two
operations of heating, and diminishing the volume, might equally
well be carried on simultaneously ; but perhaps the changes may
be more clearly understood by conceiving the two processes as
kept distinct, and, considering their effects, separately. In this
way, as the temperature and pressure are augmented, the gaseous
part is always increasing in density, and the liquid part is dimin-
ishing in density, till at last the two come to have the same density
with one another, and then they are perfectly alike in every
respect, all distinction between them having vanished.

At this stage the temperature is 31° Cent., and the pressure is
about 75 atmospheres. Above this temperature of 31° no change
of pressure can cause gasification or liquefaction; and above this
pressure of about 75 atmospheres, no change of temperature can
cause gasification or liquefaction.

[Then follows as in No. 46, supra.]

1872] THE TRIPLE POINT 297

48. ON RELATIONS BETWEEN THE GASEOUS, THE LIQUID, AND
THE SOLID STATES OF MATTER.

[From the Report of the British Association, Section A, Brighton,
1872, pp. 24—30.]

THE object of this paper is to submit some new theoretical
considerations which constitute a further development of one
portion of the views offered, at last year's Meeting of the Association,
by the author, in his paper entitled "Speculations on the Continuity
of the Fluid State of Matter, and on Relations between the Gaseous,
the Liquid, and the Solid States." He has now to make reference
to the abstract of that paper printed in the Transactions for last
year at page 30 * ; and, in particular, to the diagram of three
curves shown sketched in fig. 1 of that abstract.

In respect to these curves several essential features had been,
at the time of last year's Meeting, clearly discerned, and were
pointed out and reasoned on by the author in his paper then read.
His attempt to sketch out the curves, however, in such a way as
that they should be in agreement with the known conditions then
taken into consideration, soon forced on his attention the question
whether the two curves, one of which is that between gas and
liquid, and the other is that between gas and solid, ought to be
drawn crossing as represented here in fig. 1 a, or as in fig. 1 6 ; and
his object at present is to give a demonstration, subsequently
developed, showing that they must cross as in fig. la; or, in other
words, as in the diagram which he gave in the abstract of his last
year's paper.

It is to be understood that AX and AY are the axes of co-
ordinates for pressures and temperatures respectively; A, the
origin, being taken as the zero for pressures, and as the zero for
temperatures on the Centigrade scale; and, for simplicity in
expression and in thought, the diagram may be taken as relating
to the particular substance of water, steam, and ice, rather than
to substances in general. The curve ETP is the boiling-line, or
the line which has its successive points such that for any one of
them the two coordinates represent a pressure and temperature
for a boiling-point, or a pressure and temperature which the water
and steam can have when in mutual contact. It may also be

* [Supra, p. 286.]

298

CONTINUITY OF STATES IN MATTER

[48

called, for brevity, the steam-with-water line. In like manner the
curve NTQ is the steam-with-ice line ; and the curve MTR is the
water -ivith-ice line. The full meaning of these diagrams may
become more distinctly intelligible to the reader if he will advert
to the explanations given in the paper already referred to in last
year's Transactions, as to fig. 1 in that paper, — explanations
which, though now useful, need not be wholly repeated here, as
the present paper is meant to be read in connexion with that
previous one.

If we now look to fig. 1 a and suppose that we have water and
steam in mutual contact, the pressure and temperature must be

Fig. la.

Fig. 17;

represented by the coordinates of some point of the steam-with-
water curve LTP. Let us now suppose that we lower the
temperature gradually while keeping water and steam in mutual
contact : the point whose coordinates show the successively co-
existent temperatures and pressures will pass downwards along
the steam-with-water curve LTP. Let us suppose this operation
continued so far as to bring this point into that part of the curve
which belongs to temperatures below that of the triple point T*.
This supposed extension of the steam-with-water curve into
temperatures below that of the triple point, where freezing would
certainly set in if any ice were present, is to be conceived of as a

* The meaning of the " Triple Point " is explained in the paper already referred
to in last year's Transactions, p. 32 [p. 289].

1872] THE TRIPLE POINT 299

curve corresponding to states of equilibrium between the steam
and water. It is well known that water can, in various circum-
stances, be reduced in temperature below its freezing point without
its freezing; and this the author attributes to a difficulty of making
a beginning of change of state *. It is also known that the presence
of a gaseous atmosphere, of common air with aqueous vapour in
contact with water, does not necessarily introduce any condition
which will give liberty to the water-substance to make a beginning
of change of state into ice, either from the liquid or the gaseous
part, or from both at their face of contact. Thus there can
scarcely be a doubt but that the steam-with-water curve, LT, has
a practically attainable extension past T; and valid reasoning,
the author thinks, may certainly be founded on the supposition
of this curve as one of equilibrium between steam and water,
whether or not, in various modes of experimenting, it might be
easy or difficult or unmanageable to practically exclude all con-
ditions which would give liberty to make a beginning of the
formation of ice. We may then see that, supposing steam and
water to be present together in a condition of temperature and
pressure represented by any point such as G in fig. 1 a, there is
perfect freedom for the transition either way between water and
steam. That is to say, while the water and steam are maintained
at the temperature and pressure of the point G, the water is
perfectly free to change to steam, and the steam is perfectly free
to change to water. Let, for brevity, the temperature and pressure
of the point G be denoted by t± and pl respectively.

Now, to aid our conception in a process of theoretical reason-
ing, let us imagine an apparatus possessing certain qualities in
theoretic perfection, thus: — (see fig. 2).

Let there be a cylinder, standing upright, closed at bottom,
open at top, and with a piston which works without leakage and
without friction.

Let the weight of the piston, together with the atmospheric
load on it, be balanced by a counterpoise B ; or else let the whole
apparatus be conceived to be enclosed in a large external vessel
from which the air has been extracted, and then the counterpoise

* In papers by the author (Proceedings of Royal Society, Nov. 24, 1859, p. 158
[supra, p. 222]; and British Association Report, Transactions of Sections, 1859,
p. 25), the principle of attributing such phenomena to a difficulty of making a
beginning of change of state was, so far as he is aware, first announced.

300

CONTINUITY OF STATES IN MATTER

[48

B must just balance the weight of the piston. Let weights A,
A be laid on the piston, which will give exactly the pressure p1
to the fluid enclosed in the cavity of the cylinder ; and let this
enclosed fluid be supposed to be water-substance taken at first in
the state of steam with water, as shown in the figure, where S is
steam and W is water.

Let the entire cylinder and its contents be maintained at the
temperature ti (a temperature below that of the triple point) by
immersion in a bath at that temperature, t1} as shown in the
figure.

Fig. 2.

Now apply an infinitely small extra weight on the piston, so
that the internal pressure becomes p^ + 8, where 8 is infinitely
small. This causes the steam to go perfectly gently down to
water.

1872] THE TRIPLE POINT 301

Now insert a particle of ice. Brisk action or agitation instantly
sets in. Thus : —

(1) The water with ice cannot repose without both coming
to the temperature which, for the pressure pr + 8, or we may here
as well say for the pressure pl , belongs to water with ice ; that is
to say, in reference to fig. la, the water with ice cannot repose
without both coming to the temperature of the point U on the
water-with-ice line in that figure.

(2) The water at this raised temperature, or at any of the
intermediate temperatures between this and the temperature ti
of the surrounding bath, is in a state tending to ebullition into
steam, a state in which boiling will ensue if a beginning be made
at all, or if due facility to begin be afforded in any way.

(3) Conduction of heat, or conduction with convection, is
briskly going on, conveying heat out to the bath, since the
temperature inside is at some parts warmer than the bath, and is
nowhere cooler.

Now, either ebullition ensues, or it does not.

First. Suppose it not to take place : —

Parts of the water are warmed by the freezing-process. They
briskly transmit heat out to the bath, the freezing goes briskly
on, and the same process of transmission of heat from a higher to
a lower temperature goes briskly forward. This continues till all
the enclosed fluid has become ice.

Now it is obvious that if there is a brisk action, with rapid
conduction of heat, when steam, or water-substance partly steam
and partly water, is allowed to pass into the state of ice while the
pressure is pi + & and the surrounding temperature is t1} there
could be no return or reversal to the old condition of steam, or of
steam with water, caused or allowed by merely an infinitely small
abatement of pressure from pl + 8 to pl . To cause the ice to evapo-
rate, or to get it to remain in equilibrium with steam, which we
know experimentally it can do at a low enough pressure, a finite
(not infinitely small) abatement of pressure is necessary.

Thus has been proved what was wanted, provided we be right
in supposing ebullition not to take place.

But now : —

Second. Suppose ebullition to ensue on the introduction of
the ice — a complicated interaction of water, steam, and ice, in-
volving brisk agitation, must set in. At any face of contact of

302 CONTINUITY OF STATES IN MATTER [48

water and ice, the temperature must be that of the point U in
fig. la ; at any face of contact of steam and ice the temperature
must become that which belongs to the pressure p± on the steam-
with-ice line, and which is shown at the point W in fig. la on the
supposition of the curves crossing as represented in that figure ;
and at any face of contact of steam with water the temperature
must be that of the point G. As yet we need not assume that
we know whether the point W for pressure pl on the steam-with-
ice line is at a higher temperature than that of (7, as is represented
in fig. la, or at a lower temperature than that of C, as it would
be if the curves crossed as in fig. 16 ; but clearly we kirow that
the temperature of U is higher than that of C, which is the same
as that of the bath ; and we can also see that any steam in contact
with water and surrounded with the bath at temperature ^ while
the pressure is pl will be ready to condense to water, or will actually
so condense if the pressure be increased by the infinitely small
augmentation S,just as did the steam originally supposed to occupy
part of the cavity. Thus we must have an action going briskly
on, involving rapid conduction of heat, an action involving the
continual conversion of water-substance from the fluid state
(gaseous or liquid) to ice, and which goes on till no steam remains
to condense to water at a face of contact with water, and till no
water remains to be frozen at a face of contact with ice. As this
process goes on with briskness or agitation, involving rapid
conduction of heat, we can see that, as in the previously supposed
case, the process is irreversible by an infinitely small abatement
of pressure ; and we can see that to get steam to remain in repose
in contact with ice at the temperature ^ of the surrounding bath,
we must have the pressure abated by a finite amount, so as to be
decidedly less than the pressure p± belonging to steam with water
at the fixed temperature of the bath : that is to say, for a tem-
perature below the triple point the pressure of steam with ice is
less than the pressure of steam with water.

Hence, referring to fig. la, we see that in the steam- with-ice
curve the point D, having the same temperature ^ as the point C
of the steam-with-water curve has, must, while situated in the
isothermal line BD passing through C, be away from C at the
side where the pressure is less than at G ; or it must lie between
C and the coordinate axis YA produced past A.

This may be regarded as very nearly establishing that the

1872] THE TRIPLE POINT 303

curves cross one another, as drawn in fig. la. It shows that they
do not, as in fig. 16. Up to the present stage, however, the
reasoning does not exclude the suppositions : — 1st, that the curves
might meet tangential ly in the triple point T, and pass on without
crossing ; 2nd, that they might cross in the triple point, meeting
each other there tangentially ; 3rd, that the steam- with-ice line
might absolutely stop short in the triple point.

The first and second of these remaining suppositions, depending,
as they do, on supposed tangential meeting instead of meeting or
crossing angularly, the author thinks very unlikely. One reason
is that the condensed water-substance in contact with the steam
makes a perfectly sudden change in its character in changing from
water to ice or from ice to water ; and he therefore thinks that in
the curve which represents steam with water above the triple
point, and steam with ice below it, we should expect to find a
sudden change of direction at the point where this great physical
change suddenly takes place.

Another reason against the first of these suppositions will be
given in what follows almost immediately, by a proof that after
meeting in the triple point in rising from lower temperatures,
they cannot go on further without crossing. The third sup-
position, namely, that the steam-with-ice line might stop short in
the triple point, the author thinks very unlikely to be the truth ;
but he is not aware of any experimental proof to offer against it.

Now, that the curves, after meeting in the triple point in
rising from lower temperatures, cannot go on further without
crossing, will be proved if it be shown that on the supposition
of the steam-with-ice curve not stopping short 011 rising to the
triple point, it must, on passing that point, have its course on the
side of the steam-with-water curve remote from the coordinate
axis YA ; or, in other words, if it be shown that, for any temperature
t.2 above the triple point, the pressure of steam with water is less
than the pressure of steam with ice.

This can easily be done by a demonstration quite like the one
already given for a temperature below that of the triple point ;
and a brief sketch of it will here suffice.

Let us imagine that we have a cavity of variable dimensions,
such as a cylinder with a piston which can be loaded so as to
apply any desired pressure to fluid substance enclosed within.
Let this vessel contain steam with ice at a temperature t2) \vhich

304 CONTINUITY OF STATES IN MATTER [48

is above that of the triple point; and let the cylinder be immersed
in a bath maintained constantly at the temperature t.2. Let the
pressure of the steam with ice for this temperature be called p.2.

Now increase the pressure by an infinitely small amount 8,
making it pz + 8. While this is kept applied to the steam, the
steam is by it kept going down to the state of ice ; and thus we
can conceive of the whole or any desired part being converted
quite gently to ice*. Next, while maintaining the pressure p.2 or
pz + S in the steam, if any remains, or in the water next to be
introduced, introduce a particle of water. Instantly the ice begins
to melt, and falls in temperature, at the place of contact with
water, to the temperature of water with ice for the applied
pressure p2 or p2 + 8 ; that is, to the point V in the figure. But
the surrounding bath is warmer than this, and so a decided
difference of temperature is maintained, involving a rapid con-
duction of heat from the warmer bath to the colder melting ice
and the cold water in contiguity to that ice. There can be no
repose till all the water-substance originally enclosed as steam
with ice has become water; because, while the steam can pass
gently to ice under the pressure p.2) on the supposition that some
particle of ice is kept present, and will be forced down by the
infinitely small excess of pressure 8, the ice must briskly rush to
the state of water. But we know we can have steam present in
repose with water at the maintained temperature t2 if we make
the pressure small enough. An infinitely small abatement of
pressure will not counteract or reverse the change which has been
briskly taking place ; and so the pressure must be made decidedly
lower than either p.2 + 8 or p2 to allow of the water resting in equi-
librium in contact with steam at the temperature tz.

That is to say, referring to fig. la, on any isothermal line,
such as FG, the point H, where it is cut by the steam-with-water
line, must be nearer to the axis YA than is the point G, where it
is cut by the steam- with-ice line.

This, then, closes the course of reasoning entered on hitherto
in these pages, and establishes (the author thinks with very little
if any room left for doubt) that the two curves do not cross as in
fig. 16 ; and that in meeting at the triple point, they do not meet

* The fact that the ice being rigid would oppose a mechanical obstruction to the
complete pressing of the steam down to ice by a piston, may be noticed in passing,
but it does not introduce any theoretical difficulty into the reasoning.

1872] THE TRIPLE POINT 305

and pass tangentially without crossing, but that they must cross
as in fig. la.

The conclusion here arrived at the author thinks may admit
of experimental verification ; and he thinks it opens a desirable
field for further and more perfect experimental researches than
have hitherto been made on the coexisting pressures and tempera-
tures of steam and other gaseous substances, each in contact with
its own substance, either in the liquid or in the solid state, at
temperatures ranging above and below the triple point for each
substance. Without its being necessary to make experiments on
substances in the conditions represented by the dotted extensions
of the curves past the triple point, he thinks that very accurate
experiments might show, for steam, an obtuse re-entrant angle or
corner at T, in the line LTN, which appears not to be one curve,
but two distinct curves meeting in T, and crossing each other at
that point.

Through an examination which the author has made of the
experimentally derived curve given by Regnault* for what is
shown as LTN here in fig. la, he finds that the curve seems to
show a slightly perceptible feature of the kind here anticipated —
a slight re-entrant angle, or at least a slightly flattened place, or
place of diminished curvature at the triple point ; but this feature
does not appear sufficiently marked to admit of its being relied
upon as a decisive experimental confirmation of the theoretical
view here submitted.

The author also submitted to the Meeting the following
additional considerations on the subject.

It can easily be shown that the perpetual motion would be
theoretically attainable unless (1) the pressure of steam with ice
for a temperature tlt which is below the triple point, were less
than the pressure of steam with water for the same temperature
£j ; and also (2) unless the pressure of steam with water for a
temperature t2, taken above the triple point, were less than the
pressure of steam with ice for the same temperature t2.

To prove the first of these, we have to observe that at tl} which
is below the triple point, in pressing steam down into water, we
give mechanical work to the substance (call this a). Then when
we insert ice, there is a finite difference of temperatures, with
conduction of heat out to the bath; now by making this heat
* Memoires de VAcademie des Sciences, 1847, plate viii.

T. 20

306 CONTINUITY OF STATES IN MATTER [48

pass, not by conduction, but through a thermodynamic engine (an
air-engine for instance), we can obtain work, which let us call b.
During this freezing, too, we get back from the water-substance
a little work, owing to the expansion of the water in freezing
under the pressure pl (call this c). Next allow the volume to
increase while arranging that the ice shall be evaporating into
steam under the temperature of the bath ^ ; we obtain mechanical
work, which call d.

Now if, in this expanding process of ice to steam, the pressure
were as great as plt which was the pressure during the compressing
to water, we would get back on the whole from the piston* all the
work we gave to it ; that is, the two portions c and d of work got
back would together be as much as we gave, namely a ; and we
would have made a clear gain of the work 6 obtained from the
thermodynamic engine.

A like proof could be given in respect to the second case —
that in which the temperature is above the triple point.

A slight extension of this reasoning will prove that the curves,
in crossing at the triple point, cannot cross tangentially.

This can be seen obviously from the consideration that the
work obtainable by the thermodynamic engine is proportional to
the difference of the temperatures between which the heat is
transmitted ; and that the difference between the work given to
the piston of the cavity in compressing steam to water, and that
obtained back again during the evaporation of the ice to steam,
and then pressing the steam when the evaporation is complete a
little down till it attains again its original pressure and volume,
will be proportional, very approximately, to the difference of the
pressures existing during the compression of steam to water, and
the expansion of ice to steam, which latter pressure let us now
call pi. Also let us call the temperature of the triple point t0.

Thus it is obvious that we must have, as long as we keep very
near the triple point,

p1-pi'<xt0-t1.

And this shows that the crossing of the curves must be angular,
not tangential.

The author further suggested that the reasoning here adduced
may be followed up by a quantitative calculation founded on
experimental data, most if not all of which are already available,
by which calculation the difference of the pressures of steam with

1873] GASEOUS, LIQUID, AND SOLID STATES OF WATER 307

water and steam with ice for any given temperature very near the
triple point may be found with a very close approximation to the
truth.

49. A QUANTITATIVE INVESTIGATION OF CERTAIN RELATIONS
BETWEEN THE GASEOUS, THE LIQUID, AND THE SOLID STATES
OF WATER-SUBSTANCE.

[From the Proceedings of the Royal Society, No. 148, 1873.]

IN two communications made by me to the British Association
at its Meetings at Edinburgh in 1871*, and at Brighton in 1872f,
and printed as abstracts in the Transactions of the Sections for
those years, considerations were adduced on relations between the
gaseous, the liquid, and the solid states of matter. The new
subject of the present paper constitutes a further development of
some of those previous considerations ; and a brief sketch of these
is necessary here as an introduction for rendering intelligible what
is to follow.

Taking into consideration any substance which we can have in
the three states, gaseous, liquid, and solid, we may observe that,
when any two of these states are present in contact together, the
pressure and temperature are dependent each on the other, so
that when one is given the other is fixed. Then, if we denote
geometrically all possible points of temperature and pressure
jointly by points spread continuously in a plane surface, each
point in the plane being referred to two axes of rectangular
coordinates, so that one of its ordinates shall represent the tempera-
ture and the other the pressure denoted by that point, we may
notice that there will be three curves — one expressing the relation
between temperature and pressure for gas with liquid, another
expressing that for gas with solid, and another expressing that for
liquid with solid. These three curves, it appears, must all meet
or cross each other in one point of pressure and temperature
jointly, which may be called the triple point J.

* [Supra, p. 286.] t [Supra, p. 302.]

J In making this statement, that it appears that the three curves must all cross
each other in one point, I would wish to offer it here (as I previously did in the
1871 British- Association paper) subject to some reserve in respect of conditions not

20—2

308 CONTINUITY OF STATES IN MATTER [49

The curve between gas and liquid, which may be called the
boiling-line, will be a separating boundary between the regions of
the plane corresponding to the ordinary liquid and those corre-
sponding to the ordinary gaseous state. But by consideration of
Dr Andrews's experimental results (Phil. Trans. 1869), we may see
that this separating boundary comes to an end at a point of tempera-
ture and pressure which, in conformity with his language, may be
called the critical point of pressure and temperature jointly; and
we may see that, from any liquid state to any gaseous state, the
transition may be gradually effected by an infinite variety of
courses passing round the extreme end of the boiling-line*.

The accompanying figure [fig. la, p. 298] serves to illustrate
these considerations in reference to transitions between the three
states, the gaseous, the liquid, and the solid. The figure is
intended only as a sketch to illustrate principles, and is not drawn
according to measurements for any particular substance, though

yet known with perfect clearness and certainty. I have to suggest that we might
not be quite safe in assuming that, within a cavity containing nothing but pure
water-substance partly gaseous, the melting temperature and pressure of ice
solidified from the gaseous state would be the same as the melting temperature
and pressure of ice frozen from the liquid state, and in making other suppositions,
such as that the same quantity of heat would become latent in the melting of equal
quantities of ice formed in these two ways, and in neglecting conceivable but,
I presume, as yet imperfectly known distinctions of capillary conditions between
ice amply wet with water and ice only moistened with the last vestiges of water
before the whole liquid may be either evaporated or frozen. It might be a question
in like manner whether we can be sure that there can be theoretically a condition
of repose in a cavity containing only perfectly pure water- substance in which the
three states are present together, each in contact with the other two, so that there
would be ice partly wet with water, and partly dry in contact with gaseous water-
substance, or steam as it may be called, while the water and steam were also in
contact with each other. I offer these remarks by way of caution, as they force
themselves into notice when we attempt to sketch out the features of the three
curves under consideration, and because they may serve to suggest questions for
experimental and theoretical investigation which may have been generally over-
looked before. In the present paper, however, I proceed on assumptions, such as
are usually tacitly made, of identity in the thermal and dynamic conditions of
pure ice solidified in different ways, assumptions which, so far as is known, may
be, and probably are, perfectly true ; and I proceed on the supposition that there
can be theoretically the condition of repose here alluded to, of the solid, liquid,
and gaseous states, present together each in contact with the other two— and
consequently that the three curves would meet or cross each other in one point,
which I have called the triple point.

* Mention of this condition has been already made in a former paper by me in
the Proceedings of the Eoyal Society, November 16, 1871, p. 2 [supra, p. 279].

1873] GASEOUS, LIQUID, AND SOLID STATES OF WATER 309

the main features of the curves shown in it are meant to relate in
a general way to the substance of water, steam, and ice. A X and
A Y are the axes of coordinates for temperatures and pressures re-
spectively; A, the origin, being taken as the zero for pressures and
as the zero for temperatures on the Centigrade scale. The curve L
represents the boiling-line terminating in the critical point E.
The line TM represents the line between liquid and solid. It is
drawn showing in an exaggerated degree the lowering of the
freezing temperature of water by pressure, the exaggeration being
necessary to allow small changes of temperature to be perceptible
in the diagram. The line TN represents the line between the
gaseous and the solid states of water-substance. The line LTN
appears to have been generally (in the discussion of experimental
results on the pressure of aqueous vapour above and below the
freezing point) regarded as one continuous curve; but it was a
part of my object in the two British- Association papers referred
to, to show that it ought to be considered two distinct curves
(LTP and NTQ) crossing each other in the triple point T.

In the second of the two British- Association papers already
referred to (the one read at the Brighton Meeting, 1872)*, I gave
demonstrations showing that these two curves L T and NT should
meet, as shown in the accompanying figure, with a re-entrant
angle at T, not with a salient angle such as is exemplified in the
vertex of a pointed arch, and offered in conclusion the suggestion
that the reasoning which had been adduced might be followed up
by a quantitative calculation founded on experimental data, by
which calculation the difference of the pressures of steam with
water and steam with ice for any given temperature very near the
triple point may be found with a very close approximation to the
truth.

In the month of last October (October, 1872) I explained to
my brother, Sir William Thomson, the nature of that contemplated
quantitative calculation : I mentioned to him the method which I
had prepared for carrying out the intended investigation, and
inquired of him for some of the experimental data, or data already
deduced by theory from experiments, which I was seeking to
obtain. On his attention being thus turned to the matter, he
noticed that the desired quantitative relation could be obtained
very directly and easily from a simple formula which he had given

* [Supra, p. 302.]

310 CONTINUITY OF STATES IN MATTER [49

in his paper on the Dynamical Theory of Heat, Transactions of
the Royal Society of Edinburgh, March 17, 1851*, § 21 (3), to
express the second law of thermodynamics for a body of uni-
form temperature throughout, exposed to pressure equal in all
directions.

That formula is ^ = CM'}

at

in which p denotes the amount of the pressure, and dp/dt its rate
of increase per unit increase of temperature, the volume being
kept constant; C denotes Carnot's function; and M denotes the
rate of absorption at which heat must be supplied to the substance
per unit augmentation of volume, to let it expand without varying
in temperature. The body may be either homogeneous throughout,
as a continuous solid, or liquid, or gas ; or it may be heterogeneous,
as a mass of water and aqueous vapour (i.e. steam), or ice and
water, or ice and aqueous vapour (i.e. steam).

Now apply that formula, 1st, to steam with water, and, 2nd, to
steam with ice, the temperature of the heterogeneous body in
each case being that of the triple point ; or we may, for the
present purpose, say 0° Centigrade, which is almost exactly the
same. It is to be observed that while in the general application
of the formula the rate of increase of the pressure with increase of
temperature, when the volume is kept constant, has been denoted
by dp/dt, yet in each of the two particular cases now brought
under consideration, it is a matter of indifference whether the
volume be kept constant or not ; because the pressure of steam in
contact either with water or with ice, for any given temperature,
is independent of the volume of the whole heterogeneous body; so
that the change of pressure for change of temperature is indepen-
dent of whether there be change of volume or not. As C is a
function of the temperature which has the same value for all
substances at the same temperature, it has the same value for the
two cases now under consideration. Hence, retaining for the first
case (that, namely, of steam with water) the same notation as
before, but modifying it by the use of an accent where distinction
is necessary in the second case (that of steam with ice), and thus
using dp/dt to denote the rate of increase of the pressure per unit
increase of temperature for steam with water at the triple point
(0° Centigrade nearly), and M to denote the rate of absorption at
* [Sir Wm Thomson, Math, and Phys. Papers, Vol. i, p. 187.]

1873] GASEOUS, LIQUID, AND SOLID STATES OF WATER 311

which heat must be supplied to a body consisting of steam and
water at the triple point, per unit augmentation of volume of that
whole heterogeneous body, to let it expand without varying in
temperature, and using dp'/dt and M' to denote the corresponding
rates for steam with ice at the triple point, we have

dp Idtf _ M_
dtl dt~M''

The latent heat of evaporation of one pound of water at the
freezing point (or triple point) into steam at the same temperature,
as determined by Regnault, is 606 '5 thermic units, the thermic
unit being here taken as the heat which would raise the tempera-
ture of one pound of water one degree Centigrade ; and the latent
heat of fusion of ice is about 78 or 79 of the same thermic units.
Hence, though M and M' belong each to a cubic foot of steam at
the triple point, not to a pound mass of it, still the ratio M/M' is

606
~ 79 + 606 '

Her dp/dp'_ 606 _1_

dt/ dt~ 79 + 606" 1-13*

This shows that for any small descent in temperature from the
triple point (where the pressure of steam with ice is the same as
that of steam with water), the pressure of steam with ice falls off
1*13 times as much as does the pressure of steam with water.

In submitting the quantitative calculation now given, I have
preferred to adopt the method proposed and* developed by my
brother rather than that which I had myself previously devised,
because his method is simpler, and brings out the results more
briefly by established principles from existing experimental data.
I may say, however, that the method devised by myself was also a
true method, and that I have since worked it out to its numerical
results, and have found that these are quite in accordance with
those brought out by my brother. The two indeed may be
regarded as being essentially of the same nature ; and I think it
unnecessary to occupy space by giving any details of the method
I planned and have carried out. Its general character may be
sufficiently gathered from the concluding passages of the British-
Association 1872 paper, as printed in the Transactions of the
Sections, Brighton Meeting*.

* [Supra, pp. 305, 306.]

312 CONTINUITY OF STATES IN MATTER [49

In order to discover whether the feature now developed by
theoretical considerations is to be found showing itself in any
degree in the experimental results of Regnault on the pressures of
steam at different temperatures*, I have made careful examina-
tions of his engraved curve (plate viii of his memoir), and of his
empirical formulae adapted to fit very closely to the results
exhibited in that curve, and of his final Tables of results at the
close of his memoir ; and by every mode of scrutiny which I have
brought to bear on the subject (in fact by each of some seven or
eight varied modes) I have met with clear indication of the
existence of the expected feature ; and by some of them J have
found that it can readily be brought prominently into notice.
The engraved curve drawn on the copper plate by Regnault
himself is offered by him as the definitive expression of his experi-
ments, as being an expression which satisfies as well as possible
the aggregate of his observations — subject, however, to a very
slight alteration, which he has pointed out as a requisite amend-
ment in the part of the curve immediately below the freezing point,
a part with which the investigations in the present paper are
specially concerned.

After telling (page 581) of the great care with which he had
marked the curve on the copper plate and got it engraved, he
says : — " Je n'ai pas pu eviter cependant quelques petites irregu-
larites dans les courbes; mais une seule de ces irregularites me
parait assez importante pour devoir etre signalee. Elle se presente
pour les basses temperatures comprises entre 0° et — 16°; la courbe
creuse trop vers 1'axe des temperatures, elle laisse, notablement
au-dessus d'elle, toutes les determinations experimentales qui ont
ete faites entre 0° et — 10°. Ainsi les valeurs, que cette petite
portion de la courbe donne pour les forces elastiques, sont un peu
trop faibles, et j'ai eu soin de les augmenter, de la quantite
convenable, dans les nombres que je donnerai plus loin." Whether
we are now to think that this bend downwardsf of the curve
towards the axis of temperatures, involving what Regnault regarded
as a small faulty departure of his drawn curve from his actual
experiments, was introduced merely by a casual want of accuracy

* Kegnault, " Des Forces Elastiques de la Vapeur d'Eau aux diff ^rentes Tempe'-
ratures," Memoires de VAcad&mie des Sciences, 1847.

f In M. Eegnault's curve the temperatures are measured horizontally across
the sheet, and pressures are measured upwards.

1873] GASEOUS, LIQUID, AND SOLID STATES OF WATER 313

in drawing, or whether we may suppose that possibly there may
have been some experimental observations which attracted the
curve downwards, but were afterwards rejected on a supposition of
their being untrustworthy, it appears that such a bend is a feature
which the curve really ought to possess, and is one which even
after being partially smoothed off by way of correction is not
obliterated, but still remains clearly discoverable in the final
numerical tables of results.

This is best brought to light by means of the empirical
formulae devised and employed by Regnault for the collating of
his results. He proceeded evidently under the idea of the curve
being continuous in its nature, so that a single formula might
represent the pressures of aqueous vapour throughout the whole
of his experiments ; but before seeking for such a formula he
proceeded to calculate several local formulae of which each should
represent very exactly his experiments between limits of tempera-
ture not wide apart; and afterwards he worked out several
general formulae, each adapted singly for the whole range of his
experiments.

In regard to the one of these general formulas which he
designates as formula (H)*, he says that it represents the aggregate
of his determinations of the pressures of the vapour of water,
referred to the air-thermometer, and extending between the
extreme temperatures of — 33° and + 232° with such precision
that there could not be any hope of attaining to representing
them better by any other mode of interpolation, because the
differences, he says, between the calculated numbers and the
numbers deduced from his graphic constructions are always
smaller than the probable errors of observation. Still, for making
out his final general Table of pressures of steam for every degree
of the air-thermometer from — 30° to 4- 230°, he used three local
formulas, finding that by them he could get slightly closer agree-
ments with his experimental determinations than by using the
single formula (//) for the whole range. Thus between —32°
and 0° he used his formula designated as (E) ; from 0° to 100° he
used his formula (D) ; and between 100° and 230° he used his

* This and other formulae in M. Regnault's memoir are here referred to only by
their letters of reference, because to cite the formulae themselves with their neces-
sary accompanying explanations, would extend the present paper to too great a
length ; and any person wishing to scrutinize the formulas would naturally prefer to
have recourse to the original memoir.

314 CONTINUITY OF STATES IN MATTER [49

formula (H). He points out (page 623) that he might have
calculated this Table throughout its entire extent by the single
formula (H), and that he would thus have got almost identically
the same values by it from 100° down to 40° as those he calculated
by the formula (D), but that between +40° and —20° the pressures
given by the formula (H) would be slightly too small. This gives
indication of the existence of the feature which it is my object at
present to bring into view ; and an examination of the column of
Differences in Regnault's Table on his page 608, adapted for
comparing the pressures got from experiments as expressed by
his graphic curve with those got from the formula (H)* shows
distinctly a re-entrant angle, or at least a flattened place, in the
curve at or about 0°. Several other like comparisons, by means
of his other formulae, give like indications ; but most of these may
for brevity be passed over without further mention here. The
most decisive indication comes out in the following way. We
may observe that for temperatures adjacent to the freezing point
and extending both ways from it, Regnault finally adopted as fitting
best to his experiments the formula (E) for temperatures descending
from 0°, and the formula (D) for temperatures ascending from 0°.
He tried (at pages 598, 599 of his memoir) the continuing of the
application of his formula (D) beyond the inferior of the two limits
0° and 100°, for which he had specially aimed at adapting it to his
experimental determinations ; and he found that in calculating by
it the pressures which it would give for temperatures below 0°,
these pressures come out always slightly in excess of those which
were given by his experiments. I have developed this mode of
comparison in a more complete manner, and have arrived at
remarkable results. The formula (D) may be regarded as the
formula for giving the pressure p of steam with water, and (E) as
that for giving the pressure p' for steam with ice. The following
two Tables show the pressures p and p for temperatures, in each
case, both below and above the freezing point, as calculated from
these two formulae ; and they show, also in each case, the conse-
quent differences of pressure for 1° change of temperature at
several different temperatures, or, what is the same, the values of
dp/dt and dp'/dt for several temperatures slightly above and
slightly below the freezing point.

1873] GASEOUS, LIQUID, AND SOLID STATES OF WATER 315

TABLE I. By Formula (D); Steam with Water.

Temperatures

Pressures =p

Differences for 1°,
which are values of dp/dt
for intermediate
temperatures

Temperatures to which
the values of dp fit
belong

-3°

3-703

I '280

-2i°

-2°

3-983

)

I -298

-IF

-1°

4-281

)

1 "319

_ 1°

0°

4-600

(

I -340

+ ¥

+ 1°

4-940

\

I -362

+ 14°

+ 2°

5-302

)

I -385

+ 24°

+ 3°

5-687

(

TABLE II. By Formula (E); Steam with Ice.

Temperatures

Pressures =p'

Differences for 1°,
which are values of dp'jdt
for intermediate
temperatures

Temperatures to which
the values of dp'jdt
belong

-3°

3-644

I '297

-8J"

-2°

3-941

)

I '322

-14°

— 1°

4-263

)

t -347

- |°

0°

4-610

5

( -375

+ 4°

+ 1°

4-985

)

\

( -405

+ 14°

+ 2°

5-390

)

( -437

+ 2^°

+ 3°

5-827

)

From these two Tables we obtain the following values of

-Jr/-Tr ^s deduced from Regnault's formulae (j9) and (E).
d/t / dt

316

CONTINUITY OF STATES IN MATTER

[49

TABLE III.

Temperatures

-Si'

+ 4°

Values deduced for
dp' /dp
dt dt

375

340
405
362
437

385

-™

= 1-12

i-n

~

This gives for -»r/-j7 at the freezing point the value of about

CtC / Cut

T09 or I'lO ; while its value brought out in the earlier part of the
present paper by my brother's quantitative calculation was 1*13;
and so the feature expected shows itself here in Regnault's
results almost in the full extent in which theory shows that it
ought to exist.

Regnault gives in the same memoir (page 627 and following
pages) another Table, one intended chiefly for meteorological
purposes, and in which the pressures are stated from — 10° to
4-35° for every -fa of a degree. In this Table the numbers
inserted as representing the pressures below the freezing point
are slightly different from the corresponding ones in his general
Table already referred to ; and he mentions that this slight
discrepancy has resulted from the fact that the two Tables were
formed at different periods, and were not calculated by the same
formula ; but he remarks that the differences are insignificant, as
they scarcely amount to '02 millimetre. Here, too, as in the
general Table, the feature expected shows itself, though in a
diminished degree. By a careful examination of its column of
Differences for y1^ of a degree, and by making a few small
arithmetical adjustments which may be regarded as amendments
in the way of interpolation in that column, I find that, according

1873] GASEOUS, LIQUID, AND SOLID STATES OF WATER 317

to the experimental results as they are represented in this Table,
the value of-l-/- at the freezing point would come out to be

about 1*05 or T06. We have seen by the new calculation, based
on theory, in the present paper that it ought to be T13; so here the
feature is found showing itself in about half the degree in which,
according to the new quantitative calculation, it ought to be met
with. When we consider that Regnault's reductions of his experi-
mental results in the making out of curves, formulae, and tables
for representing them in the aggregate were, as we have sufficient
ground to suppose, carried out under the idea, now proved to be
erroneous, of there being, for aqueous vapour, continuity in
variations of pressure with variations of temperature past the
freezing point, just as past any other point of temperature, and
when we further consider that the quantities with which we are
here concerned are indeed very small, it is not surprising that
there should have been a tendency to smooth off this feature on
the supposition that any departures of the experimental observa-
tions from the course of a continuous or smooth curve were only
slight irregularities due to experimental errors or imperfections.

It may now, in conclusion, be remarked that if from experiments
independent of those which have been made, or may be made,
directly on the pressure of aqueous vapour at different temperatures
near the freezing point, both above and below it, very correct
determinations of the values of the quantities C, M, and M ' can
be made, such determinations will lead to more correct evaluations
of dp/dt and dp'/dt for aqueous vapour in contact in the one case
with liquid water, and in the other with ice, than we at present
possess. Such determinations, we may presume further, would, if
very trustworthily arrived at, conduce to the attainment of a more
correct estimate of the density of steam at the freezing point (or
at the triple point) than we now possess. In fact, in connexion
with the subject which has been here under consideration, there
are various important quantities so connected that improved
determinations of one or more of them may lead to more correct
evaluations of others.

318

CONTINUITY OF STATES IN MATTER

[50

50. RELATION BETWEEN GASEOUS AND LIQUID STATES [UN-
PUBLISHED NOTES BEARING ON ANDREWS'S EXPERIMENTS].

[May 2Ist and 22nd, 1862.]

IN order to show at least some arbitrary limits to gases and
liquids, as distinguished from their substance in a fluid state which
can scarcely be called distinctively either a liquid or a gas :

Temperatures

Fig. 1.

Let aaa be the curve of total heat of the liquid at its boiling
point and of the gas at saturation :

Let bb be that one of the curves of total heat for the various
temperatures when the pressure is constant, which touches the
foregoing curve aaa. Then, according to one arbitrary assump-
tion, we might say that the condition of the fluid expressed by the
space A to the right of the latter curve is one of fluidity which is
neither to be called liquid nor gaseous distinctively, because no
addition nor abstraction of heat while that pressure is maintained
will make the fluid either boil off or condense. Still according to
another view we might call the fluid at A a liquid, because by
simply diminishing the pressure without altering the total heat,
either 1st without adding or abstracting heat, or 2nd while keeping
total heat the same by making an addition of heat to correct for
the heat disappearing as work, we may make it boil off. In this
process the evaporation would produce such cold as to keep a

1862] CONTINUOUS TRANSITION FROM GAS TO LIQUID 319

portion liquid while another portion gets an increase of total heat
at its expense and becomes a gas. On getting to B the fluid
divides into two parts. One starts to G and passes towards C'.
The other goes towards B' but keeps always as it goes giving off
portions up to the curve (7(7'.

On the other hand, if the fluid began by going from D to E
without addition or diminution of heat from an external thermal
source, any further diminution of pressure will cause one part to
condense while the other will continue on the upper branch of the
curve going from E towards C", but always obtaining its accession
of total heat (if the form of the curve requires that*) by the
deposition of some of itself as liquid.

Consider next the passage from G to H by diminution of
pressure and then the separation along the two branches: — a
separation into gas and liquid without boiling or condensation.

Consider and describe what happens when pressure is con-
tinuously altered for a constant temperature : by passing along
lines LM, NO, PQ. In the line LM we shall arrive at a place
where an infinitely small increase of pressure will expel a large
finite quantity of heat accompanied by a sudden diminution of
volume, after which the expulsion of heat and diminution of
volume become very slow. In the line NO I expect (if the curve
has not a cusp) that we shall meet with a place of extremely rapid,
at one point infinitely rapid, expulsion of heat and rapid falling
down of volume (temperature being constant) then by further
increase of pressure we get a very slow expulsion of heat and
diminution of volume. In PQ nearly the same, but gradual.

[June 6th, 1862.]

As the forms of the various curves which I have sketched on
previous papers on this subject are uncertain and can only be
determined by experiment, it is to be observed that the sketching
of those curves is as yet useful chiefly to aid in the consideration
of experimental observations ; and that while some of the features
of these curves are already indicated approximately by Dr Andre ws's
experiments, it is necessary to guard against deducing conclusions
from assumed forms of any of these curves as delineated partly at

* The study of this may lead to some conclusions as to the relative forms of
the two branches of the curve.

320

CONTINUITY OF STATES IN MATTER

[50

random in advance of experiments*. The sketching of probable
features or approximate forms of these curves may serve useful
purposes in indicating desirable courses for experimental investi-
gation.

The foregoing being borne in mind as to the uses of such
kinds of sketches of curves, I think the following curves will
deserve consideration.

10

29 30 31 32

centigrade

Temperature

Fig. 2.

These curves mean those of volumes for varying temperatures
and each curve being for a constant pressure pl or p.2 or ps or p4 or
p5. The chief feature that I mean here to show is the relation
between the wave in p4, p5 and p6 as compared with the abrupt
rise in^!, p2 and ps.

The experiments of Dr Andrews (whether or not those of
Cagniard de la Tour did) show that there is a certain superior limit
of temperature above which the fluid carbonic acid does not show

* [The first brief report by Andrews on the influence of very high pressures on
the more permanent gases is a short condensed note in Report of Brit. Assoc. 1861;
he communicated a brief statement of the discovery of the critical point for carbonic
acid to Miller's Chemical Physics in 1863: the first " Bakerian Lecture" (Phil.
Trans.) on the continuity of the liquid and gaseous states was published in 1869 —
see Introduction thereto, reprinted in Andrews' Scientific Papers, p. 297. The
marked lowering of the critical point by admixture of a small portion of non-
condensable gas was communicated to the Eoyal Society in 1875, and the second
"Bakerian Lecture" in 1876.]

1862] CONTINUOUS TRANSITION FKOM GAS TO LIQUID 321

any sudden transition from " liquid " to " gas," or rather does not
arrive at any point of total heat beyond which it refuses to take
more diffused through it, and sends all additions of heat only to
parts of itself, leaving the remainder unchanged.

Now it seems clear that we have a similar superior limit of
pressure, so that for pressures above that limit we meet with no
discontinuity in the possible volume or in the possible quantity of
heat.

[June 9th, 1862.]

Having now cut ou't in wood* a curved surface to exhibit, and
to aid the further consideration of my view of, the relation between
liquids and their gases, or rather of the various conditions of
pressure, temperature, volume, and quantity of heatf in which a
fluid can exist, I shall here note a few points on the subject.

1st. It is only by experiment that the exact form of the
curved surface can be found; but some of the facts of the case
being already certainly known it is possible already to carve or mould
some of the chief features of the curve surface, and these may serve
to aid in showing the courses along which further experimental
researches might best be directed, and also to aid in understanding
the correlation of experimental results; and to aid in forming
opinions in advance of experiments as to what is likely to result in
intermediate cases between various experimental results which
may already or at any time be arrived at.

2nd. It has occurred to me to look for what may be the
nature of the discontinuity of the increase of volume with increase
of temperature at the boiling point for any given pressure ; and
I now note for consideration the question whether it may not
perhaps be the case that the curves, when the constant pressure
for each of them is low enough to admit of boiling or of the
existence of the fluid in two different states of density or in two
different states of quantity of heat per unit of mass, have a fold
over themselves as shown by dotted curved junctions a^, a2a2)
asa3.

With reference to this it is to be observed that, in the curve

* [See figures from photographs, p. 277.]

t June 14. It is to be observed that this model for giving the relation between
pressure, temperature and volume aids in considerations of quantities of heat, but
that a separate model is intended to give the quantity of heat in terms of pressure
and temperature.

T. 21

322

CONTINUITY OF STATES IN MATTER

[50

1862] CONTINUOUS TRANSITION FROM GAS TO LIQUID 323

for pressure pl for instance, while the boiling point for the pressure
Pi is at BB'y it is possible to heat the liquid to a higher tempera-
ture without making it boil till arrival at some point of temperature
b, where it boils with bumping and from which the temperature
falls to B when the steam and water are present together. This
observed fact, of the liquid being capable of being raised above its
boiling point without boiling, makes it reasonable to suppose that
the curve AB does not terminate abruptly at B but may be
continued; and my present suggestion is that it seems not unlikely
that the curve would really be continued by a^a^ so as to be
continued as B'G. In reference to this it seems to me that it will
be important to ascertain whether steam can possibly be cooled
below its regular condensing point for its pressure without its
condensing. I think probably this has never yet been properly
examined into ; and has probably been never ascertained. To test
the point fairly precautions would require to be taken to have no
water present along with the steam, in order that the steam might
experience a difficulty of making a beginning of its change of state
if the occurrence of such difficulty be possible. The internal
surface of the enclosing vessel, too, might require special prepara-
tion to avoid anything that could set the steam off to change to
water.

If the hypothesis here suggested, as to there being something
in nature corresponding to the dotted junctions a^, a2a2, asa3)
between the curves AB and B'G, &c., be correct (though at present
it is merely a suggestion for examination) it may further be con-
sidered whether or not there may in any circumstances be a possibility
of changing from a liquid to its gas by passing along a curve a^alt
or a2a2, or asa3. If so, it would seem that in a properly prepared
vessel containing only a liquid, and that being kept at a constant
pressure, we might by continuously adding heat, get 1st, a rising
temperature and increasing volume, then 2nd, a falling temperature
and increasing volume, then 3rd, a rising temperature and increasing
volume, and then have vapour at the boiling temperature for the
pressure.

If the dotted curves a^, &c. have a real existence, I suppose
they will represent possible but unstable states of the fluid : —
states which perhaps men cannot bring into occurrence : unless
perhaps in some extreme or special circumstances.

A reason in favour of the supposition of the existence of the

21—2

324 CONTINUITY OF STATES IN MATTER [50

dotted junctions is that (so far as I can judge from Dr Andre ws's
experiments hitherto made) it seems probable that in passing
from heavy pressures to light pressures, as from the heavy pressure
p6 to p5 and jt?4 successively, there is a point of steepest slope in
each of the curves (that is a point of inflexion) and that in the
successive curves the steepness of the slope or the angle of the
tangent to the abscissa at that point goes on increasing from
curve to curve till it becomes 90° : and then it would seem
probable that the angle would go on increasing beyond 90° in
which case the curve would stand thus : —

Origin,

Temperatures >

Fig. 4.

PROPOSED EXPERIMENT WITH REFERENCE TO PART OF THE
FOREGOING. To take a glass phial or hollow globe such as a
Florence flask. Put a thermometer into it, put water in and
draw the mouth down to a small aperture which can be easily
hermetically sealed. Immerse the flask in a bath at 213° Fahr.
or so (a little above boiling temperature). The water will boil off
and carry out all air with the steam. Melt the tube so as to close
it. Then the flask contains only steam : or steam with a little
water which may perhaps have condensed in the tube but which
it might be well to avoid allowing to be there, unless in very small
quantity. Then immerse the whole in a bath at say 220° Fahr.
or at a high enough temperature to make quite sure that not a
molecule of water is left in the liquid state. Then remove the
flask from the bath, or better allow the bath very gradually to
cool, and watch the enclosed thermometer. It will of course sink
gradually. Watch particularly to see whether after sinking to a
certain extent it rises again suddenly. If such rise be found to
occur it will take place at the moment of the commencement of
condensation of water from the steam ; and if it occur it will prove
that the steam had been cooled below its boiling point without

1862] CONTINUOUS TRANSITION FROM GAS TO LIQUID 325

condensing, and that on the commencement of precipitation of
water or dew the difficulty of making a beginning was got over
and the boiling point for the existing pressure was assumed.

[June 14, 1862.]

In respect to the curve shown thus on former papers ; I now
observe that it is simply the projection, on a plane parallel to the

Curve for saturated
Steam

Origin

Temperatures

Fig. 5.

reference line of temperature and the reference line of total heat,
of the abrupt edge of the curve surface which gives the quantity
of heat as a function of the temperature and pressure; — that
abrupt edge being the line where the sudden transition takes
place from gas to liquid or liquid to gas.

It will be a matter of great interest to discover the relations of
pressure, temperature and volume, and of pressure, temperature
and total heat for a given substance (carbonic acid for instance),
through so wide a range of pressures and temperatures as to
introduce the change from either liquid or gas to solid. There
will be in each of the two general curve surfaces which represent
by their ordinates the volume and the total heat as functions of
the temperature and pressure, two abrupt places; — one for the
change from gas to liquid, and the other for the change from
liquid to solid; — but as, at ordinary atmospheric pressure, the
change occurs at once from gas to solid, without liquefaction, it is
clear that these two abrupt places will merge into one as the
pressure diminishes from very high pressures down towards one
atmosphere.

In reference to the idea of there being perhaps a possibility of
cooling steam or other vapours below their ordinary saturation

326

CONTINUITY OF STATES IN MATTER

[50

points of temperature ; it strikes me that perhaps a film of clean
oil washed completely round the inside of the hermetically sealed
glass globe or flask containing the liquid or vapour might give
the requisite kind of surface for withholding whatever may tend
to give freedom to change of state from gas to liquid. My im-
pression at any rate is that I have often seen on a piece of glass
or other substance dew deposited at some parts, while none gets
a beginning of forming itself at others; — the difference being
associated essentially with differences of cleanness, &c. of the glass
or other surface. As to the deposition of hoar frost on scratched
lines on a window in preference to other parts there is no do^bt.

Intensely Cold radiating
Surface or M material

Cork may be far away from flask so as to give a long hot tube AB.

Fig. 6.

Brief, hasty memorandum of idea which has occurred to me
for devising a method for use in case it be found that no kind of
internal surface whatever enclosing the steam can be obtained
free from sufficing to give by its contact, perfect freedom to the
steam to begin to change its state to water. The method consists
in keeping the internal surface slightly above the boiling point of
temperature, and making the internal part of the steam cooler by
radiation. If any such method is to succeed, I think it will be
necessary to avoid having any thermometer in the middle of the
flask, because the glass of the thermometer, I presume, would be
cooled by the radiation so as to be quite as cool as, or cooler than, the
surrounding steam cooled by the same radiation. It strikes me
(but I have not yet properly considered this) that the steam itself
might be used like an air thermometer with due precautions by its

1869] CONTINUOUS TRANSITION FROM GAS TO LIQUID 327

expansion or contraction which might give indications in the hot
tube AB\ perhaps by acting on a piston of mercury in that tube.

This page and foregoing are mostly taken from an old scribbled temporary
pencil note of some years ago which was not meant to be kept, except till I
should note the subject better. J. T., 29 March 1868.

NOTES AND QUERIES. — ON GASES, LIQUIDS, FLUIDS.

[Primary date 10th May, 1869.]

Various conversations with Dr Andrews in recent weeks,
and at least one new experimental result of his (showing a
" critical point " in mixed air and carbonic acid) together also with
my having recently attained to a somewhat better understanding
and clearer views of some principles or theoretical reasonings as to
molecular attraction in capillarity, have led me in the last few
weeks to give much consideration to the nature and relations and
distinctions among the Gaseous and Liquid states of fluids, and
the transitions between those states.

I believe I have arrived at some new and improved views; and
further developments of old views; and I now intend to note down
some views which I have come to hold as being either true or as
being at least suppositions or hypotheses worthy of further study
and research.

I proceed on the hypothesis of the substance dealt with,
whether called Gas, Vapour, Liquid or Fluid ; or at one part of
itself Gas or Vapour, and at another part Liquid; being of the
nature of a compressible fluid in every part down to the smallest
parts that are to come into account ; or in other words I shall not
go on any supposition of gases being made up of separate particles
repelling one another and leaving greater or less void spaces
between them according as the gases are more expanded or more
reduced in volume. I shall treat the matter as if from every point
in the fluid to every other, no matter how near they be, down to the
smallest distances that require consideration for the matters in
question, the fluid is continuous as a fluid : — and as if the fluid
everywhere possesses an expansive tendency, so that pressure
must everywhere be received by the fluid on one side of a dividing
surface (or as I call it interface) from the fluid, or solid, on the
other side, to prevent the fluid from expanding indefinitely, or to
balance its expansive force. I proceed on the basis of supposing

328 CONTINUITY OF STATES IN MATTER [50

that it is either true ; or that it closely enough, for present
purposes, resembles the truth ; to suppose that contiguous parts of
the fluid press on one another by forces applied at their faces of
mutual contact, distributed over those faces, and that molecular
attractions, very powerful in the case of liquids, act between all
portions of fluid that are very near one another : the attractive
force from any one material point to any small portion or mass of
adjacent fluid having its points of application distributed every-
where in the substance of that attracted mass.

In a gaseous fluid at its condensing point of pressure and
temperature it may be said that in some sense a state of instability
is arrived at : because in that condition further reduction of the
space confining the whole mass does not cause compression of
every part of the fluid, but the fluid separates into two parts in
different states of density and of total heat per unit of mass. The
one part undergoes no change whatever; — meets with no com-
pression ; — and the diminution of the whole volume influences the
other part alone by giving it diminished volume or increased
density; but in fact neither the one part nor the other of the
separated parts undergoes any change except in this that a further
reduction of the whole volume causes portions of the gaseous part
to change to the denser state of the liquid part. The kind of
instability which, apparently at least, is arrived at, or in some
sense is actually arrived at, is of this nature : — that if we conceive
without the transformation of any part of the gaseous fluid to
liquid, any further reduction of volume without change of tem-
perature to be effected, the gaseous fluid will be in a state in
which it cannot practically remain ; at least in which so far as at
present known to me, or I suppose to anybody, it cannot be got to
remain, and certainly unless with very special arrangements will
not remain ; but out of which it will pass by one part going down
in volume to the liquid state and the other reverting to its
original density and pressure, the original temperature being
understood to be maintained, say, by immersion in a bath of
constant temperature.

Thus practically we may be right or very nearly right in
representing the case of the gas compressed to its condensing
point of temperature and pressure, as having just arrived at the
verge of instability so that it cannot practically (by ordinary
means at least) be further compressed at its constant temperature

1869] CONTINUOUS TRANSITION FROM GAS TO LIQUID 329

because a state of complete practical instability would then be
entered on and a part would collapse to liquid while another
would revert to the gaseous state at the verge of condensing.

Now it appears to me that this practical instability really does
not hold good in principle in a gas at its condensing point if we
consider the gas as totally free from contact with any solid or
liquid : this supposition is practically impossible, but I am not
sure that it would be impossible to devise some means of actually
getting the gas brought to a temperature and pressure below the
condensing point by some method that might be analogous to
methods used by Donny and others to get perhaps water above its
boiling point without boiling, or below its freezing point without
freezing*. In principle I think the gas without presence of water
or of any solid or liquid dense substance is not in an unstable state
when cooled and pressed to below its ordinary condensing point.

In fact I think that in a gaseous fluid at its condensing point
of temperature and pressure we have not the condition that any
further compression would make it collapse to the liquid state : or
we have not the condition that if the adjacent parts be brought
nearer together, their attraction will overcome the expansive force
and cause collapse : but for causing the condensation it is necessary
to have dense matter in close proximity : such dense matter may
be either the solid containing vessel, or some of the fluid in its
liquid state. I think it probable however (and I hope to find it
to be the case) that a perfectly dry interior of a containing vessel
with perhaps some specially prepared face, may give less freedom
for the beginning of the change of state from gaseous to liquid
than would a portion of the liquid itself in contact with the gas.

Now see fig. Y. The shaded part represents (according to my
idea) a bar of continuous fluid normal to and passing through the
surface or rather the lamina of demarcation : — one end of the
bar being gaseous and the other liquid, and the transition along
the bar from gas to liquid being perfectly gradual by a gradually
increasing pressure and density. The lamina of demarcation
extends from aa to bb. Now at any such depth as cc the fluid
(as I think) is subject to far more pressure and has far more

* Qy>, might this be effected in steam by allowing rapid expansion in a super-
heated vessel as in a steam engine cylinder completely jacketed? Does not the
expansion of the steam ivhile performing work cause it to pass partly into the liquid
state? and might not perfect jacketing prevent the beginning of liquefaction ?

330

CONTINUITY OF STATES IN MATTER

[50

density than those due at the condensing point to the tempera-
ture : and yet it does not collapse : but on the contrary is quite
ready to rise in volume to the gaseous state on any retirement
of the insistent bar of gas; such retirement being however un-
accompanied by any reduction of the gaseous pressure.

Ordinates represent •
density

Fig. 7.

Memo written at Largs, Dec. 31, 1869. — Be careful to recollect that throughout
this diagram, the pressure as contemplated in Dr Andrews's Experiments and in
my wooden curve surfaces * would be CONSTANT. It is the abutting push that varies
here in descending from the gas into the liquid.

Now further we can see how raising temperature and pressure
jointly we arrive (under the present theory or hypothesis) at a
critical point: — that which Dr Andrews has found experiment-
ally:—

* [See figures from photographs, p. 277.]

1869] CONTINUOUS TRANSITION FKOM GAS TO LIQUID 331

By raising the temperature of the whole mass of fluid, and
increasing the pressure at the same time so as to retain the same
portion of the mass as before still gaseous; and the same part
liquid as before ; the consequence of applying the heat must be
that the liquid part will expand in volume and get less density;
so that it will have less molecular attraction and will attract less
than before the fluid in the lamina of transition per unit of mass
of that fluid. This would allow that fluid to expand and disperse
or go off were there not a pressure applied from without sufficient
to give increased density to the whole gas in spite of the expanding
tendency of the heat. Now by having denser gas than before at
about the gaseous side of the lamina of transition we can attain
to the requisite pressure in the middle of the lamina in spite of
the diminished density of the liquid : — the liquid less dense than
before attracting the gas more dense than before being able to
give to the intervening fluid the requisite pressure and density,
even though these require to be more than before. Thus the
gaseous part will be more pressed, and instead of being allowed to
expand will actually become more dense than before; and will
have increased molecular attraction ; and, by our carrying forward
far enough the augmentation of temperature and of corresponding
pressure, we must ultimately (under the theory I am giving)
arrive at a stage of temperature and corresponding pressure at
which the gaseous part and the liquid part shall have the same
density, and then the molecular attractive cause of difference of
density in the two parts will no longer exist, but the distinction
will have faded away.

It appears to me to be very important now to get what I may
call the prevalent prejudice eradicated from people's minds, under
which people usually imagine or tacitly assume the pressure applied
to a gas by its confining vessel as being the pressure in the gas.
The so-called " Law of Mariotte" is not a law of nature in any
sense. First because Natterer's experiments show that when a
density such as that of liquids is attained by air, the volume is
several times as great as it should be if Mariotte's law held good
for the relation between the applied pressure and the volume.

Secondly we must specially guard againsfc taking Mariotte's law
even if amended or modified to adapt it so that it amended, or the
new formula substituted for it, would express the relation between
density and applied pressure ; — against taking that altered or

332

CONTINUITY OF STATES IN MATTER

[50

amended formula as showing the expansive force in terms of the
density (or what is the same in terms of the volume). The
expansive force which is the real pressure is altogether different
from the applied pressure : and the one does not vary proportion-
ally to the other during the compression of air or oxygen or
hydrogen or other commonly called perfect gases, nor of steam,
carbonic acid or other condensible gases.

When Natterer applied 2700 atmospheres to a gas : — he may
so far as can now be known have increased its molecular attraction
millions of times : but we do not at present know, for the gas to
begin with, what the amount of the pressure due to mofecular
attraction was, over and above the applied pressure : — so we cannot
at present express the molecular attraction (I think) in atmospheres
either in the gas in its large state at atmospheric applied pressure,
or when under the applied pressure of 2700 atmospheres.

Curve for constant temperature is [not*] impossible as here
drawn below. Because from n up to m we would have at constant
temperature an increase of pressure giving an increase of volume,
which I think obviously cannot bef.

* A little later I see that it is not impossible in principle, only that equilib.
would be unstable ; equilib. of gas alone would be stable from a to m, . ... fluid
alone or in the single state unstable .... liquid alone stable. [Author's MS. here
partly torn.]

t [The considerations developed in these MS. memoranda are recapitulated in
Clerk Maxwell's Theory of Heat at the end of Chapter vn. See also Prof. Thomson's
paper, No. 46, supra p. 278, from Proc. Roy. Soc. 1871. Maxwell, and Clausius
later, afterwards pointed out that the line in the figure marked condensing point of
pressure must cut off equal areas on its two sides.]

1869] CONTINUOUS TRANSITION FROM GAS TO LIQUID 333

Supposition.

I assume as admitted, or proceed hypothetically on supposition,
that the pressure due to molecular attraction, or added by it to
that applied by the containing vessel, is as square of the density
at the place. Water at ordinary boiling point is about 1728 times
as dense as its steam; 1*7 282 = 3,000,000; so that the pressure
due to molecular attraction in the water would be about three
million times as much as that due to molecular attraction in
the steam.

DYNAMICS AND ELASTICITY

51. ON THE STRENGTH OF MATERIALS, AS INFLUENCED BY THE
EXISTENCE OR NON-EXISTENCE OF CERTAIN MUTUAL STRAINS*
AMONG THE PARTICLES COMPOSING THEM.

[From the Cambridge and Dublin Mathematical Journal, November 1848,
pp. 252 — 258. This paper is also reprinted, with a few changes made
in it with the author's concurrence, in Article "Elasticity," by Sir William
Thomson, in Encyclopaedia Britannica, 9th Edition, Vol. vn. pp. 798 —
800.]

MY principal object in the following paper is to show that
the absolute strength of any material composed of a substance
possessing ductility (and few substances, if any, are entirely devoid
of this property), may vary to a great extent, according to the
state of tension or relaxation in which the particles have been
made to exist when the material as a whole is subject to no
external strain.

Let, for instance, a cylindrical bar of malleable iron, or a piece
of iron wire, be made red hot, and then be allowed to cool. Its
particles may now be regarded as being all completely relaxed.
Let next the one end of the bar be fixed, and the other be made
to revolve by torsion, till the particles at the circumference of the
bar are strained to the utmost extent of which they can admit
without undergoing a permanent alteration in their mutual con-
nexion f. In this condition, equal elements of the cross section

* [Note added November 1877, in Encyc. Brit, reprint by Lord Kelvin.

More nearly what is now called stress than what is now called strain is meant by
"strain" in this article, which was written before Rankine's introduction of the
word stress, and distinct definition of the word strain.]

f I here assume the existence of a definite "elastic limit," or a limit within
which if two particles of a substance be displaced, they will return to their original
relative positions when the disturbing force is removed. The opposite conclusion,
to which Mr Hodgkinson seems to have been led by some interesting experimental
results, will be considered at a more advanced part of this paper.

1848] INFLUENCE OF INTERNAL STRAIN ON STRENGTH 335

of the bar afford resistances proportional to the distances of the
elements from the centre of the bar ; since the particles are dis-
placed from their positions of relaxation through spaces which are
proportional to the distances of the particles from the centre.
The couple which the bar now resists, and which is equal to the
sum of the couples due to the resistances of all the elements of
the section, is that which is commonly assumed as the measure
of the strength of the bar. For future reference, this couple may
be denoted by L, and the angle through which it has twisted the
loose end of the bar by ®.

The twisting of the bar may, however, be carried still farther,
and during the progress of this process the outer particles will
yield in virtue of their ductility, those towards the interior
assuming successively the condition of greatest tension; until,
when the twisting has been sufficiently continued, all the particles
in the section, except those quite close to the centre, will have
been brought to afford their utmost resistance. Hence, if we
suppose* that no change in the hardness of the substance com-
posing the material has resulted from the sliding of its particles
past one another ; and that, therefore, all small elements of the
section of the bar afford the same resistance, no matter what
their distances from the centre may be, it is easy to prove that
the total resistance of the bar is now | of what it was in the
former case ; or, according to the notation already adopted, it is
now

* [Note added October 1877, Encyc. Brit.

This supposition may be true for some solids ; it is certainly not true for solids
generally. A piece of copper or of iron taken in a soft and unstrained condition
certainly becomes "harder" when strained beyond its first limits of elasticity, that
is to say, its limits of elasticity become wider ; and a similar result will probably
be found in ductile metals generally. Thus the resistance of the outer elements
will be greater than those of the inner elements in the case described in the text,
until the torsion has been pushed so far as to bring about the greatest hardness in
all the elements at any considerable distance from the axis. It may be that before
this condition has been attained the hardening of the outer elements will have been
overdone, and they may have begun to lose strength, and to have become friable
and fissured. The principle set forth in the text is not, however, vitiated by the
incorrectness of a supposition introduced merely for the sake of numerical illustra-
tion.]

f To prove this, let r be the radius of the bar, t\ the utmost force of a unit of
area of the section to resist a strain tending to make the particles slide past one
another ; or to resist a shearing strain, as it is commonly called. Also let the
section of the bar be supposed to be divided into an infinite number of concentric

336 DYNAMICS AND ELASTICITY [51

If, after this, all external strain be removed from the bar, it
will assume a position of equilibrium, in which the outer particles
will be strained in the direction opposite to that in which it was
twisted and the inner ones in the same direction as that of the
twisting, the two sets of opposite couples thus produced among
the particles of the bar, balancing one another. It is easy to
show that the line of separation between the particles strained
in the one direction, and those in the other, is a circle whose
radius is f of the radius of the bar. The particles in this line
are evidently subject to no strain* when no external couple is
applied. The bar with its new molecular arrangement n*ay now
be subjected, as often as we please^, to the couple -| L, without

annular elements ; the radius of any one of these being denoted by x, and its area
by 2irxdx.

Now, when only the particles at the circumference are strained to the utmost ;
and when, therefore, the forces on equal areas of the various elements are proportional
to the distances of the elements from the centre, we have 77 (x/r) for the force of a
unit of area at the distance x from the centre. Hence the total tangential force of

the element is

= 2irxdx . 77 (#/r),

and the couple due to the same element is

= x . 2irx dx . 77 (xlr) = 27777 (1 A") - x3dx :
and therefore the total couple, which has been denoted above by L, is

= 27777 - I x3dx,

that is, L = |7T77r3 (a).

Next, when the bar has been twisted so much that all the particles in its section
afford their utmost resistance, we have the total tangential force of the element
= 2nxdx . 77, and the couple due to the same element

= x . 2irxdx . 77 = 27^ .x^dx.
Hence the total couple due to the entire section is

0

But this quantity is f of the value of L in formula (a). That is, the couple which
the bar resists in this case is f L, or f of that which it resisted in the former case.

* Or at least they are subject to no strain of torsion either in the one direction
or in the other ; though they may perhaps be subject to a strain of compression or
extension in the direction of the length of the bar. This, however, does not fall to
be considered in the present investigation.

f This statement, if not strictly, is at least extremely nearly true : since from
the experiments made by Mr Fairbairn and Mr Hodgkinson on cast iron (see
various Reports of the British Association), we may conclude that the metals are
i nfluenced only in an extremely slight degree by time. Were the bars composed of
some substance, such as sealing wax, or hard pitch, possessing a sensible amount
of viscidity, the statement in the text would not hold good.

1848] INFLUENCE OF INTERNAL STRAIN ON STRENGTH 337

undergoing any farther alteration ; and therefore its ultimate
strength to resist torsion, in the direction of the couple L, has
been considerably increased. Its strength to resist torsion in the
opposite direction has, however, by the same process, been much
diminished : for, as soon as its free extremity has been made to
revolve backwards through an angle* of f ® from the position
of equilibrium, the particles at the circumference will have suffered
the utmost displacement of which they can admit without under-
going permanent alteration. Now it is easy to prove that the
couple required to produce a certain angle of torsion is the same
in the new state of the bar as in the oldf. Hence the ultimate
strength of the bar when twisted backwards, is represented by a
couple amounting to only fZ. But, as we have seen, it is ^L
when the wire is twisted forwards. That is, then, The wire in
its new state has twice as much strength to resist torsion in the
one direction as it has to resist it in the other.

Principles quite similar to the foregoing, operate in regard to
beams subjected to cross strain. As, however, my chief object at
present is to point out the existence of such principles, to indicate
the mode in which they are to be applied, and to show their great
practical importance in the determination of the strength of
materials, I need not enter fully into their application in the case
of cross strain. The investigation in this case closely resembles that
in the case of torsion, but is more complicated on account of the
different ultimate resistances afforded by any material to tension
and to compression, and on account of the numerous varieties
in the form of section of beams which for different purposes it is

* [Note added October 1877, in Encyc. Brit.

This assumes that the limits of elasticity in a substance which has already
been strained beyond its limits of elasticity are equal on the two sides of the
shape which it has when in equilibrium without disturbing force — a supposition
which may be true or may not be true. Experiment is urgently needed to test
it ; for its truth or falseness is a matter of much importance in the theory of
elasticity.]

f To prove this, let the bar be supposed to be divided into an infinite number
of elementary concentric tubes (like the so-called annual rings of growth in trees).
To twist each of these tubes through a certain angle, the same couple will be
required whether the tube is already subject to the action of a couple of any
moderate amount in either direction, or not. Hence, to twist them all, or what
is the same thing, to twist the whole bar, through a certain angle, the same couple
will be required whether the various elementary tubes be or be not relaxed, when
the bar as a whole is free from external strain.

T. 22

338 DYNAMICS AND ELASTICITY [51

found advisable to adopt. I shall therefore merely make a few
remarks on this subject.

If a bent bar of wrought iron, or other ductile material, be
straightened, its particles will thus be put into such a state, that
its strength to resist cross strain, in the direction towards which
it has been straightened, will be very much greater than its
strength to resist it in the opposite direction, each of these two
resistances being entirely different from that which the same bar
would afford, Avere its particles all relaxed when the entire bar is
free from external strain. The actual ratios of these various
resistances depend on the comparative ultimate resistances Afforded
by the substance to compression and extension; and also, in a
very material degree, on the form of the section of the bar.
I may however state that in general the variations in the strength
of a bar to resist cross strain, which are occasioned by variations
in its molecular arrangement, are much greater even than those
which have already been pointed out as occurring in the strength
of bars subjected to torsion.

What has been already stated is quite sufficient to account
for many very discordant and perplexing results which have been
arrived at by different experimenters on the strength of materials.
It scarcely ever occurs that a material is presented to us, either
for experiment or for application to a practical use, in which the
particles are free from great mutual strains. Processes have
already been pointed out by which we may at pleasure produce
certain peculiar strains of this kind. These or other processes
producing somewhat similar strains are used in the manufacture
of almost all materials. Thus, for instance, when malleable iron
has received its final conformation by the process termed cold
swaging, that is by hammering it till it is cold, the outer particles
exist in a state of extreme compression, and the internal ones in
a state of extreme tension. The same seems to be the case in
cast iron when it is taken from the mould in which it has been
cast. The outer portions have cooled first, and have therefore
contracted while the inner ones still continued expanded by heat.
The inner ones then contract as they subsequently cool, and thus
they as it were pull the outer ones together. That is, in the end,
the outer ones are in a state of compression and the inner ones
in the opposite condition.

The foregoing principles may serve to explain the true cause

1848] INFLUENCE OF INTERNAL STRAIN ON STRENGTH 339

of an important fact observed by Mr Eaton Hodgkinson in his
valuable researches in regard to the strength of cast iron (Report
of the British Association for 1837, p. 362)*. He found that,
contrary to what had been previously supposed, a strain, however
small in comparison to that which would occasion rupture, was
sufficient to produce a set in the beams on which he experimented.
Now this is just what should be expected in accordance with the
principles which I have brought forward : for if, from some of the
causes already pointed out, various parts of a beam previously to
the application of an external force have been strained to the
utmost, when, by the application of such force, however small,
they are still farther displaced from their positions of relaxation,
they must necessarily undergo a permanent alteration in their
connexion with one another, an alteration permitted by the
ductility of the material ; or, in other words, the beam as a whole
must take a set.

In accordance with this explanation of the fact observed by
Mr Hodgkinson, I do not think we are to conclude with him that
"the maxim of loading bodies within the elastic limit has no
foundation in nature." It appears to me that the defect of
elasticity, which he has shown to occur even with very slight
strains, exists only when the strain is applied for the first time ;
or, in other words, that if a beam has already been acted on by a
considerable strain, it may again be subjected to any smaller strain
in the same direction without its taking a set. It will readily be
seen, however, from Mr Hodgkinson's experiments, that the term
"elastic limit," as commonly employed, is entirely vague, and must
tend to lead to erroneous results.

The considerations adduced seem to me to show clearly that
there really exist two elastic limits for any material, between
which the displacements or deflexions, or what may in general
be termed the changes of form, must be confined, if we wish to
avoid giving the material a set ; or, in the case of variable strains,
if we wish to avoid giving it a continuous succession of sets which
would gradually bring about its destruction: that these two elastic
limits are usually situated one on the one side, and the other on

* For farther information regarding Mr Hodgkinson's views and experiments,
see his communications in the Transactions of the Sections of the British Associa-
tion for the years 1843 (p. 23) and 1844 (p. 25), and a work by him entitled
Experimental Researches on the Strength and other Properties of Cast Iron. 8vo.
1846.

22—2

340 DYNAMICS AND ELASTICITY [51

the opposite side of the position which the material assumes when
subject to no external strain, though they may be both on the
same side of this position of relaxation *, and that they may there-
fore with propriety be called the superior and the inferior limit
of the change of form of the material for the particular arrange-
ment which has been given to its particles ; that these two limits
are not fixed for any given material ; but that if the change of
form be continued beyond either limit, two new limits will, by
means of an alteration in the arrangement of the particles of the
material, be given to it in place of those which it previously
possessed : and lastly, that the processes employed in the Amanu-
facture of materials are usually such as to place the two limits in
close contiguity with one another, thus causing the material to
take in the first instance a set from any strain however slight,
while the interval which may afterwards exist between the two
limits, and also as was before stated, the actual position assumed
by each of them, is determined by the peculiar strains which are
subsequently applied to the material.

The introduction of new, though necessary, elements into the
consideration of the strength of materials may, on the one hand,
seem annoying from rendering the investigations more compli-
cated. On the other hand, their introduction will really have the
effect of obviating difficulties, by removing erroneous modes of
viewing the subject, and preventing contradictory or incongruous
results from being obtained by theory and experiment. In all
investigations, in fact, in which we desire to attain, or to approach
nearly, to truth, we must take facts as they actually are, not as we
might be tempted to wish them to be, for enabling us to dispense
with examining processes which are somewhat concealed and intri-
cate, but are not the less influential from their hidden character.

* Thus, if the section of a beam be of some such form as that shown in either
of the accompanying figures, the one rib or the two ribs, as
the case may be, being very weak in comparison to the
thick part of the beam, it may readily occur that the two
elastic limits of deflexion may be situated both on the same
side of the position assumed by the beam when free from
external force. For if the beam has been supported at its
extremities and loaded at its middle till the rib AB has
yielded by its ductility so as to make all its particles exert
their utmost tension, and if the load be now gradually re-
moved, the particles at B may come to be compressed to the
utmost before the load has been entirely removed.

1848] ELASTICITY AND STRENGTH OF SPIRAL SPRINGS 341

52. ON THE ELASTICITY AND STRENGTH OF SPIRAL SPRINGS,
AND OF BARS SUBJECTED TO TORSION.

[From the Cambridge and Dublin Mathematical Journal, No. xvn.
November 1848, pp. 258—266.]

A SPIRAL Spring of the most usual kind consists of a long bar
or wire, generally of a circular section, coiled up into the form of
the thread of a screw.

For the purpose of attaining precision in speaking of such
springs, the following definitions and preliminary explanations
will be useful. The curve in which the centres of all the sections
of the bar are situated may be called the spiral axis of the spring.
This lies in the surface of a cylinder, the axis of which may be
called the longitudinal axis of the spring. The angle which the
spiral axis makes with a plane perpendicular to the longitudinal
axis may be called the inclination of the coil or of the spiral.
Each end of the bar is bent in such a way that the force applied
to elongate or compress the spring may act in the longitudinal
axis*. In what follows, unless the contrary be specified, the
spring may be supposed to be suspended by one end, the force
applied being one of tension produced by a weight hung at the
lower end.

The Elasticity and Strength of Spiral Springs have not, so
far as I am aware, been hitherto subjected to scientific investi-
gation; and erroneous ideas are very prevalent on the subject,
which are not unfrequently manifested in practice by the adoption
of forms very different from those which would afford the greatest
advantages. Having had occasion to construct some spiral springs
which, in their elasticity, strength, and dimensions, should fulfil
certain definite conditions, I was led to seek for principles to

* In fact, even if, in the construction of the spring, this matter has not been
attended to, and the ends of the bar forming the points of application of the
opposite forces have not been placed in the longitudinal axis ; immediately on a
tensile force being applied, the spring will, if it be of considerable length, adjust
itself so that the force will act in that axis, except in the neighbourhood of the
two ends. At those parts the spring will be weaker than towards the middle ; and,
if the force be sufficient to induce a permanent alteration on its form, this change
will commence by the ends assuming forms of greater resistance, the longitudinal
axis approaching more nearly to the line of action of the forces.

342

DYNAMICS AND ELASTICITY

[52

guide me in determining the forms and dimensions best adapted
to accomplish the ends desired.

With this view, the first matter to be considered was the
exact nature of the strains which act
on the various parts of a spiral spring;
and the whole subject became at once
simple, as soon as I perceived that the
only strain which produces a sensible
effect is one of torsion, acting alike on
every part of the coil. To render this
clear, let us consider any section P of
the bar, made by a plane passing
through the longitudinal axis AB.
Now, when a weight w is suspended
at B, the forces transferred from one
side to the other of this section con-
sist of a couple whose force is w, and
whose arm is the distance PC from
the centre of the section at P to the
line AB, together with a force w
parallel to AB, tending to make the one side of the section
slide upon the other in the direction of the longitudinal axis.
The effect of this force must be extremely small, in fact
evanescent, compared to that of the couple ; and the force may
therefore be neglected, especially when the coefficients for the
elasticity and strength of the material are determined in the way
which will be hereafter pointed out. The slight deviation of the
above-mentioned section of the bar from a circle due to the
inclination of the spiral, may also be neglected in the theory, as
the minute influence which it may have will also be, in a great
degree, corrected for by the mode of determining the coefficients.

Let now r be the radius of the bar ; I the total length coiled
up; a the radius of the coil, or the distance from the longi-
tudinal to the spiral axis ; w any weight which may be hung on
the spring; e the elongation corresponding to that weight;
and 0 the angle through which a bar composed of the same
substance as the spring, having its length and radius each
unity, is twisted when subjected to a unit couple. This quantity
0 may be called the coefficient of deflexion by torsion for the
substance of which the bar is composed.

1848] ELASTICITY AND STRENGTH OF SPIRAL SPRINGS 343

Let the spiral part of the bar be supposed to be straightened
out, and let the bar be sup-
posed to be placed with one
end fixed at AD\ and with a
couple applied at the other
extremity by means of a weight,
equal to w, suspended at B, and
a force in the line EF equal,
parallel, and opposite to that of
w ; the arm of this couple being
equal to a the radius of the Civ\

coil.

Now it can be shown that, in bars subjected to torsion, the
angle of torsion is proportional to the length of the bar, to the
couple applied, and inversely to the fourth power of the radius
of the bar. Hence the angle of torsion in the present case, or
the angle described by EB, in passing from its natural position

to one of equilibrium with the couple wa is = 6 — — *.

Hence, the space moved over by a point at a distance a from
the centre is = 6 — — . Now a little consideration will show that

r4

this space must be equal to e, the elongation of the spiral spring

* As these principles regarding torsion have been laid down in various works
on Mechanics and Engineering, I here take them for granted. The methods of
deducing them have, however, been insufficient, as it has been, tactily at least,
assumed that all the elements in the section of a bar are free from strain when the
bar as a whole is free from external strain ; since it is assumed that when the bar
is twisted to any extent less than that which would strain its circumference to the
utmost, any equal elements of its section undergo strains proportional to the
distances of the elements from the centre. It seldom occurs, however, tliat the
real condition of a bar is in accordance with this assumption ; for I have shown in
the preceding paper that the various particles of materials usually exist under
great strains in opposite directions, which are in equilibrium with one another.
The conclusions which had previously been derived are, however, in themselves
correct ; and in a note to the paper just referred to, I have supplied the step which
was wanting in the proof by showing that the angle of torsion of a bar, or in other
words, its stiffness is not influenced by the presence or absence of internal opposing
strains among its particles ; although the case is very different with regard to
ultimate strength of the bar, which is materially altered by changes in those
strains. From this it follows that the coefficient for the stiffness or deflexion of a
bar composed of a given substance has but one value, while that for its ultimate
strength may have various values. Of this more will be said in what follows.

344 DYNAMICS AND ELASTICITY [52

due to the application of the weight w. Hence we have

e = 61^ (1).

This equation involves the conditions of the elasticity, or the
stiffness of a spring as compared with its dimensions, and the
substance of which it is composed. We will next proceed to
those of its strength and its power ; or, in other words, we will
enter on considerations connected with the greatest weight which
it can support, and the space through which it can be elongated
without rupture or permanent alteration.

In addition to the notation given above : — Let W be the
greatest weight which the spring, if its particles are all relaxed
when it is not loaded, can bear without taking a set; E the
greatest elongation, that namely which corresponds to W ; /JL the
utmost couple producing torsion which can be resisted by a bar
whose radius is unity, composed of the same substances as the
spring, and having its particles at various distances from its centre
free from mutual opposing strains when it, as a whole, is subject
to no strain. In the preceding paper, " On the Strength of
Materials," I showed that the utmost couple which can be resisted
by the bar will vary with the internal arrangement of the particles,
its greatest value being f and its least f of its mean value, which,
in the bar whose radius is unity, has just been denoted by //..
Any value of this couple, different from the mean one, adapted
to a particular arrangement of the particles, may be denoted by
jjf, and the utmost weight and elongation in a spring having a
similar arrangement may likewise be denoted by W and E'. It
will readily be seen that //, is to be regarded as the coefficient for
any given substance, of the utmost strength of a cylindrical bar
composed of it to resist torsion, when the particles of the bar have
been so arranged that they may be all relaxed when the bar is
free from external strain. It must, however, be remarked that JJL
.would still represent the strength of the bar, even though there
were some mutual opposing strains among the particles, provided
that the particles at the circumference be relaxed when the bar is
free from external strain ; and that none of the internal particles
exist under so great displacements from their positions of re-
laxation, as to occasion their being strained to the utmost sooner
than the particles at the circumference, during the twisting of
the bar.

1848] ELASTICITY AND STRENGTH OF SPIRAL SPRINGS 345

If now, in the formula L — ^irrjr3, for the strength of a bar
when it is of its mean amount, which was proved in the paper
before referred to, we take r=l,L will become what we have denoted
by JJL. Hence p - JTTT;, and the formula becomes L or the utmost
couple = yu?-3.

Again, since W is the utmost weight, and a the arm at which
this acts, the utmost couple may also be expressed by Wa. Hence
Wa — Mr3 and

(2).

The greatest elongation of which the spring can admit will
be found by substituting in (1), W for w and E for e.

To justify us in making this substitution it must, however,
be here remarked that, in ordinarily formed spiral springs, the
elongations continue proportional to the weights added, even up
to the very greatest that can be resisted. This fact I have
myself observed by an experiment conducted with considerable
care, and in which any deviation from the foregoing relation
which may have existed was less than the inaccuracies of
observation *.

Now, by making the substitution above indicated, of W for
w, and E for e, in (1) we obtain

which, by (2), may be put in the following form,

E-Op% ........................... (4).

The equations (1) and (2) together with (3) or (4) involve the
various circumstances connected with the elasticity and strength
of ordinary spiral springs. For enabling us to determine, by
means of these equations, the actual amounts of any of the

* From this two distinct conclusions may be inferred : 1st, that the angle of
torsion of a bar continues proportional to the applied couple as long as the arrange-
ment of the particles remains unaltered ; and, 2nd, that the alteration in the form
of the spring by the increase of its angle of inclination and the consequent
diminution of the radius of the coil does not produce a sensible effect. For, were
there any deviations from the relation stated in the former proposition, this must
in the experiment have been exactly counteracted by an effect of the change of
form of the spring ; which, it is clear, would have been a coincidence very unlikely
to occur.

346 DYNAMICS AND ELASTICITY [52

variable quantities concerned, when a sufficient number of the
variable quantities have been already fixed upon in accordance
with the purposes to be effected ; the constant coefficients 6 and
yu, for the substance must be determined by experiment.

Without however knowing the actual amounts, we may, by
interpreting the equations, arrive at many useful conclusions for
the comparison of the properties of springs constructed of the same
substance, but having various dimensions. From (1) we see that :

1st. If r the radius of the bar, and a that of the coil, be
fixed ; the elongation produced by any weight w will be propor-
tional to I the length rolled up to form the coil.

2nd. If a bar or wire of a certain length and radius be given
to form a spring; the elongation produced by a certain weight
w will be proportional to the square of the radius which we may
adopt for the coil.

3rd. If the radius of the bar be fixed, and the length of the
spring when closed so that the coils may touch one another, or
what is the same, the number of coils be also fixed ; I must be
proportional to a ; and therefore the elongation due to a weight
w will be proportional to the third power of the radius which we
may adopt for the coil.

4th. If the length of the bar and the radius of the coil be
fixed, the elongation due to a weight w, will be inversely pro-
portional to the fourth power of the radius of the bar which we
may adopt.

5th. With a given weight of metal and a given radius of the
coil ; the elongation, due to a weight wt will be proportional to

Z3, or inversely to r6, since I must be proportional to — .

From (4) we see that the ultimate elongation is :

1st. Proportional to the length of the bar, if the radius of
the bar and that of the coil be fixed.

2nd. Proportional to the radius of the coil, if the length and
the radius of the bar be fixed.

3rd. Inversely proportional to the radius of the bar, if the
length of the bar and the radius of the coil be fixed.

From (2) we perceive that the absolute strength of the spring,
being independent of the length, is proportional to the third

1848] ELASTICITY AND STRENGTH OF SPIRAL SPRINGS 347

power of the radius of the bar, if the radius of the coil be fixed ;
and that it is inversely proportional to the radius adopted for the
coil, if the radius of the bar be fixed.

By combining (2) and (4) we arrive at the interesting con-
clusion that the "resilience" of a spiral spring, that is the total
quantity of work which can be stored up in it, is independent of
the form or proportions of the spring, and is simply proportional
to the quantity of metal contained in the coil. For, since the
weights producing any elongations are proportional to those elon-
gations, it follows that the resilience is = \ WE.

Hence, by (2) and (4), we find that the resilience is =\6p?lrz,
which, since 9 and //. are constant, is proportional to the volume
of the coil or to the weight of metal composing it.

Many other relations might be deduced in similar ways, but
those already pointed out will suffice, as others will be readily
perceived when they may be wanted, by properly interrogating
the formulas.

For determining the values of /j, and 0 for iron wire such as
is commonly used for making spiral springs (called Charcoal
Spring Wire) ; a spring constructed of this material was subjected
to careful measurement and experiment, and the following data
were obtained :

I r = '0923 inches,

Dimensions of the spring <j I = 215*6 inches,

( a= 1/315 inches.

When the spring was successively loaded with weights, each
four pounds heavier than the one before, it was found that
56 pounds was the weight which just commenced to produce a
permanent elongation, and the elongation corresponding to this
weight was observed to be 16*9 inches. By the method which
had been employed for bending the wire into the spiral form,
and for separating the coils so that they might not press on one
another when the spring was unloaded, the wire had been put
into the condition which it would have received by having been
twisted beyond the original elastic limit, that condition namely,
in which nearly all the particles in its section would come to be
strained to the utmost at the same time. Hence, according to the
notation which has been adopted, this ultimate weight and elonga-
tion must be denoted by W and E' '; which, by the principles
given in a former paper, already referred to, will be such that

348 DYNAMICS AND ELASTICITY [52

W shall be equal to, or rather less than, JTF,
and E' equal to, or rather less than, f E*.

By taking W, fjtf, and E'] for TT, ^, and E in equations (2) and
(3), we get

from which, by the foregoing experimental data, we obtain

6 = 0-000,000,059 f and / = 94,000.
But fjf is equal to, or rather less than, |. Hence

V

p, = 70,000, or rather more.

The values here assigned to 6 and yu, will, I think, be found
quite sufficiently accurate for all practical purposes ; especially
as the metal, in other cases, cannot be assumed to be of exactly
the same quality as that used in the present one. The experi-
ment from which these values have been deduced is the only
one I have as yet been able to make ; I hope, however, as soon
as circumstances may permit, to carry out a consecutive series of
comparative experiments with springs of various dimensions and
forms and of several different kinds of metal, and also to make
corresponding experiments by subjecting to direct torsion, bars
similar to those forming the springs. In this way would be found
the amount by which the coefficients may vary in accordance
with different circumstances ; and, in applying the formulas
afterwards to any particular case, we should be able to choose
such values of the coefficients as might appear most suitable ; or
at least we should know what degree of dependence ought to be
placed in results obtained by applying the formulas to such cases.
If a spring having the radius of the bar very small compared to

* If we could be sure that the twisting of the wire, before the experiment, had
been sufficiently great, it might be stated with certainty that W' = $W, and E' = %E.
The uncertainty in this respect, though it cannot much affect the resulting value
of /*, is the greatest to which the present determination of the coefficient /x is
subject.

f It may here he observed that for the determination of 6 the extreme weight
and elongation W and E' should not have been used, unless it had been found
that these would lead to the same results as any smaller weight and elongation w
and e. It was however found, as has been already stated, that the elongations
were throughout proportional to the weights applied ; and therefore it is a matter
of indifference what weight and corresponding elongation we adopt for the deter-
mination of 6.

1873] SAFETY AND DANGER IN STRUCTURES 349

that of the coil, and having the angle of its spiral as small as
possible, were used, there can be no doubt but that the coefficients
so obtained would agree very closely with those deduced from
experiment by direct torsion.

Before concluding, I shall now merely remark that, according
to the principles already given, spiral springs should always be
made of bars of circular section, since such bars have a much
greater resilience* when subjected to torsion than others whose
section is different. Thus we see that the rectangular section
which has been frequently adopted in large spiral springs for
railway carriage buffers is very disadvantageous. It has probably
been derived from the idea that the bar is subjected to a trans-
verse strain ; an idea which, however erroneous, is the one that
usually presents itself to persons considering in a cursory manner
the action of spiral springs.

53. ON THE PRINCIPLES OF ESTIMATING SAFETY AND DANGER
IN STRUCTURES, IN RESPECT TO THEIR SUFFICIENCY IN
STRENGTH.

[Lecture delivered as introductory to the course of Civil Engineering and
Mechanics in the University of Glasgow, in Session 1873-4.]

IT is a frequent remark with parents and teachers, that it
augurs ill of a boy when he tends too much to ask the cui bono
question — to ask what is the use of his tasks in Latin and Greek,
or of his studies in Euclid or Algebra. To a certain extent that
remark holds good. It is often better for a youth to trust to
others that a course of learning may likely be valuable to him in
the future, than to let opportunities for learning slip past through
his being over-careful against the trouble of learning things unless
their utility to himself has been first clearly and certainly shown.
At the period of life, however, at which you whom I now address
have arrived, and when you have entered on a course of Engineer-
ing, intended, as it is, especially for practical applications, I think
the cui bono question is often a very proper one, and I think that,
as much as possible, you should aim at having in view at least

* The meaning of the term " resilience " was before stated to be the quantity
of work which can be stored up in the material, by giving to it its utmost change
of form.

350 DYNAMICS AND ELASTICITY [53

some practical uses for most of the subjects which occupy your
attention or engage your labours.

Holding this view, I have selected, for an introductory lecture,
a subject which I think may with advantage be brought before
your minds at this early stage, as showing or suggesting some of
the important practical uses of the detailed studies in strength
and elasticity of materials, and arrangement of structures, to which
your attention will subsequently be directed. The lecture may
be briefly entitled —

ON THE PRINCIPLES OF ESTIMATING SAFETY AND DANGER IN
STRUCTURES, IN RESPECT TO THEIR SUFFICIENCY IN
STRENGTH.

The sources from which dangers in the employment of struc-
tures may arise are almost infinitely numerous and varied, and no
brief discussion of them is possible. Even with structures perfectly
sufficient in strength for their legitimate uses, dangers may arise
in the management of them through casualties, misunderstandings,
negligences, and many other faults or misfortunes of people. It
is not of such things that I propose to treat on the present
occasion. I do not intend to refer at present to safety or danger
as involved in the methods of organizing and conducting active,
busy, and complicated operations or processes, such as the traffic
of railways and steamboats, or the industrial work in factories.
In short it is on points respecting safety and danger as involved
in the adaptation of matter rather than in the management of
men that on the present occasion I propose to treat.

I wish, specially, to turn attention to the means which can be
used, and either are, or ought to be used, for arriving at our
opinions or judgments on the sufficiency or insufficiency of some
of the most important, and some of the most common structures
on which the lives of the public generally, or of many of its
members, must necessarily be often staked. As examples of the
class of structures to which I allude, I may cite steam-engine
boilers, iron and timber bridges, floors, cranes, ships, water
reservoirs, and numerous small things involving more or less of
danger, as, for instance, slating of roofs, chimney tops on houses,
and gasaliers with their counterpoise weights, which, like the
sword of Damocles, hang threateningly over our heads from day
to day.

1873] SAFETY AND DANGER IN STRUCTURES 351

The modes of judging of the sufficiency of structures are
mainly of two kinds :

1st, By calculating, or guessing what the capabilities of the
structure are likely to be, on the supposition of the material being
good, and free from important flaws ; and trusting to the care of
the maker, and to such inspection as may be practicable, for
avoiding original defects, or subsequent dangerous deterioration.
And, 2nd, By testing or proving the sufficiency originally, and at
suitable times subsequently. My main object is to advise, and to
assign reasons for the recommendation, that the latter method, the
one by actual testing, should be used generally in cases in which
it is practicable, in preference to the former alone.

It must, however, be understood that it is indeed only in a
small proportion out of the whole number of cases occurring in
practice, that any very definite or reliable testing can be carried
out. We cannot, for instance, proceed to test a ship as to its
capability of resisting in all its multitudinous parts, the varied
and unknown violences to which it may probably sometime be
subjected by winds and waves; and, perhaps, by sandbanks and
rocks in addition. For railway carriage wheels, axles, springs, &c.,
in like manner, we can arrange no very accurate or precise tests ;
for this reason, among others, that, where shocks and tremors are
concerned, we have no sufficient knowledge of what stresses or
forces the material may be subjected to in its several parts; and
that such violences as those just now mentioned often bring about
their destructive effects by gradual accumulations of injury, as, for
instance, by the introduction of local over-straining, or incipient
cracking, which will gradually increase.

The method of testing besides, even in the cases to which it is
applicable, cannot supersede the calculating, or, in many cases,
merely guessing what may probably be required for sufficiency,
because the structures must first be made before they can be
tested ; and in the original designing of them the best principles
of calculation, or of scientific estimation, would still have their
most legitimate scope. Even when well designed and carefully
constructed, however, or presumed to be so, in many cases the
structures cannot or ought not to be regarded as either perfectly
or in a high degree safe until after they have been actually tested,
and actually found to have some very wide margin of excess of
strength beyond their utmost known or possible requirements.

352 DYNAMICS AND ELASTICITY [53

What then are we to understand by the words " safety " and
" danger " in reference to such questions as are now proposed to
be considered ? Safety and danger in structures as to their
sufficiency or insufficiency of strength, when they are to be sub-
jected to any definite or more or less indefinite forces or influences,
do not depend merely on the sufficiency or insufficiency of the
structures themselves, but they depend essentially also on our
knowledge or ignorance of whether the structure be sufficient in
strength or not so. Danger or risk consists in uncertainty ; perfect
safety as to strength consists in knowledge of sufficiency. A
structure may possess tenfold the requisite strength, but our using
it may be a very hazardous proceeding, if we do not know that it
is strong enough in its dimensions and general arrangement, or if
we have reason to doubt that it may have unascertained dangerous
faults. Let us test it, however, with a threefold or a fivefold load,
and if this does not break it nor destructively alter it, we may now
have great confidence that it is very safe for being trusted with
the smaller intended load for its ordinary use.

A rope or chain either new, or worn and damaged, hanging in
the shaft of a mine, or from the top of a building, may reasonably
be declared to be unsafe for bearing a man suspended to it in a
bucket or basket. Put on a fivefold load, and if this does not
break it, it becomes quite safe ; and yet its own strength has not
been augmented: the change is that our knowledge of its capa-
bilities has been extended and rendered more definite.

Further, in respect to our ordinary risks in the use of chains,
let us suppose that we buy a chain at a store, and we have no
ground to doubt the respectability of the people from whom we
make the purchase. We do not know whether the chain has been
proved or not, nor whether the iron in it is of very good quality or
not. The salesman says it is good, or says the makers have sold
it as of good quality. He says it is of such size as has often been
sold and used for lifting stones of a ton weight. We pay the price
of a good chain, and have not time to set about testing or proving
the strength of the chain we have bought ; but we proceed to lift
weights of one ton by it, though we are aware that we can have
no certainty that the iron in the chain is all good, nor that every
link is properly welded. In using it thus we can have no certainty
that the one ton stone may not come down with a crash ; and we
could not possibly stand below the hanging stone and regard the

1873] SAFETY AND DANGER IN STRUCTURES 353

chain as being safe for its duty. If, however, we first lift and let
down many times repeatedly three tons at a time, and then use
the same chain for one ton, we can with great confidence stand
under the hanging stone and regard the chain as being very safe.

If a plank is placed across a deep opening to serve as a
temporary passage for men — as, for instance, is constantly done
during the progress of building operations — and if the plank
appears old, knotty, or otherwise weak, a workman thinking to
cross it will consider it dangerous. Let him, however, see a load
much heavier than himself repeatedly passed over it from end
to end, and he will then regard the plank as safe for his own
weight. The change here again through which safety has been
attained, or risk obviated, is not that the plank has become
stronger, but that knowledge has been attained of its sufficiency.

Thus we may clearly observe that while the sufficiency or
insufficiency of a structure for bearing a certain load is a property
inherent absolutely in the structure itself, and does not depend on
our knowledge or uncertainty respecting it; yet the safety or
unsafety of the structure for our employment of it depends on
whether we know of its being sufficient.

In submitting to consideration the two very simple cases I
have adduced — the cases of the chain and of the plank — I wish at
the outset to cast aside a notion which is most extensively preva-
lent, and which is extremely influential in the practical determi-
nation of the degrees of mildness or severity to which tests should
be carried. It is that structures — as, for instance, boilers or
bridges — should be tenderly dealt with in testing them ; that, in
fact, the tests should not, or need not, very much exceed the
working loads, because it is alleged that if the limits of elasticity
of the material have been exceeded, if the material of the structure
has taken a permanent set or alteration of form, the material is
injured in its strength, and thus the structure may be left in a
less safe or more dangerous condition than before testing. With
the notion thus, and in various similar statements constantly put
forward, I totally disagree; and, briefly to reply to such statements,
I would say that in cases where the structure from the nature of
its material, or from any peculiarity in the combination of its
parts, can be supposed to be liable to receive cumulative injury,
or alterations of form from successive applications of the same
test load, I would have the severest desirable test repeated several

T. 23

354 DYNAMICS AND ELASTICITY [53

times, or many times successively. Then, if the structure bears
this without showing signs of failure, it must be very safe indeed
in regularly working with a small proportional part of that test
load. Because, if the structure was weakened by the first applica-
tion of the load, and had been previously too weak, much more
will it now be incapable of resisting a second application of that
same damaging load, and it will either break, or show some
permanent damage; and even if it should not absolutely suffer
rupture at this stage, yet a number of repetitions of the loading
would result in visible damage, or absolute fracture. If no such
result ensues, then, as I said before, the structure must be very
safe for its comparatively small ordinary working load.

That a piece of material, especially of a ductile or malleable
substance, such as wrought iron or copper, is not necessarily
injured, or "crippled" to use a word which has often been applied
in this respect, will become very evident when we consider a few
well known ordinary cases. For an ordinary cylindrical boiler the
plates of the cylindrical part have been all bent to their cylin-
drical form by being passed through rollers when cold, and have
thus received a set or permanent alteration of form ; yet they are
never considered as being injured or seriously altered in their
capabilities by this usage.

Again, a bellhanger brings soft copper wire into a house to use
it as material for bell wire ; but, before proceeding to adjust it
into its place for permanent service, he attaches one end to any
suitable fixed object, and pulls strongly at the other end. The
wire yields to his pull more and more as he pulls more and more
strongly, till it is permanently stretched by perhaps a fifth part
or a quarter of its original length. The wire cannot have been,
at the beginning, perfectly alike in strength at all parts. On the
pull being applied, the weakest part must yield first; that part
must become smaller in cross section, because of the stretching in
length ; yet that part does not break, but becomes actually
stronger than before, and pulls out the other parts which had not
commenced to yield in a ductile manner at first. The wire has
become much stronger, even with its diminished size of cross
section, than it was originally; for it now bears, and can henceforth
bear, without any new ductile stretching, a pull very much
greater than that to which it formerly yielded. This hardening
and strengthening process, performed on the spot where the wire

1873] SAFETY AND DANGER IN STRUCTURES 355

is to be used, rather than in the manufactory or workshop, serves,
in the case of the bellhanger, the useful purpose of producing for
him a wire straightened from such crumples and bends as would
exist in, and would be difficult to be cleared away from, a coil of
copper wire hardened by stretching previously to being brought
to the place where the wire is wanted for use.

A gasfitter twists a considerable length of block tin or lead
pipe, say, through 90° of torsion. The twist is distributed (or
rather distributes itself) over the whole length ; but if any part
twisted were thereby weakened, the further twisting applied to
the pipe as a whole would take place at the first damaged part,
and would not be spread along the whole length.

The like applies to the twisting of wire, and to the bending of
it ; and numberless other instances might readily be adduced.

Now, to return to the practical testing of structures, which I
would recommend for attainment of safety, I have to add that if
the structure be one liable to gradual deterioration from wear and
tear, corrosion, accidental injuries, or the like, as is the case, for
instance, with steam boilers, I would, at reasonable intervals of
time, repeat the process of testing for safety in its full original
severity ; and if at any time the structure should fail under a well
devised test, I would consider that it was good to have it
decisively put out of use at that stage. In instituting the tests,
I would prefer to undergo the danger of loss of the property, or
supposed value of the structure itself, rather than the danger both
to property and to life which might be consequent on the con-
tinued use of the unproved and dangerous structure.

I have here spoken of such a degree of severity as may be
suitable in a well devised process of testing for safety ; and I have
recommended the repetition, at reasonable intervals, of the same
process in its full original severity. There is, however, a distinc-
tion of practical importance which may be made between a test
for safety and an original test for another purpose. It may
sometimes be wise to make a test (called, it may be, a contract
test, or a valuation test) which may be made heavier than what is
considered necessary or suitable for repetition after wear. In a
boiler, for instance, we may want to ascertain whether or not the
new boiler sold is of such good material and workmanship as to
stand some test agreed on, which may be more than enough to
insure present safety, but may be agreed on and paid for with a

23—2

356 DYNAMICS AND ELASTICITY [53

view to provision of a sufficient margin of extra strength at first
as an allowance for subsequent deterioration by use — through
rusting, for instance, and through the injurious effects of unequal
heating and cooling in different parts, or of occasional overheating
of parts exposed to the fire. Thus, an original contract or
valuation test may often, with good reason, be made more severe
than the safety tests which may wisely be subsequently applied
from time to time.

The principle of using in some cases a valuation test as
distinct from an ordinary safety test may apply practically to
chain-cable testing, anchor testing, boiler testing, and, bridge
testing, and the list might readily be extended to numerous other
cases. The object here is to find if the thing comes up to a
certain standard of .goodness; even though in some cases — as, for
instance, in anchors and anchor chain-cables — we cannot specify-
any particular load as the working load.

Another practical case, somewhat different from any I have
hitherto adduced, may now be noticed. Hitherto I have spoken
of cases in which the object is to test things intended for use, and,
therefore, to be careful that the test shall not injure them unless
they be of bad material, or otherwise defective, so as not to possess
the desired and expected strength. But, on the other hand,
there are frequent cases in which it is both advisable and cus-
tomary to test to destruction samples selected at random from
among things supplied in large numbers intended to be alike.
Such testing serves an important use in checking against the
employment, whether knowingly or not, of materials of bad
quality.

In such considerations as those with which we are to-day
engaged, the term working load is used to denote the greatest or
most severe load to which a structure is intended to be subjected
when serving the purposes for which it is designed. Ultimate
load means the load which would just suffice to break or destroy-
ingly damage the structure. Proof load means the load applied,
or intended to be applied, in testing and proving its strength.
This last term, proof load, I must however mention, has been
sometimes used to denote the unknown greatest load against the
continued application or frequent repetition of which the structure
may be supposed to be safe, or, as it is sometimes called, proof, as
in the expressions water-proof, fire-proof, &c. The use of the

1873] SAFETY AND DANGER IN STRUCTURES 357

term proof load in this sense I regard as not to be recommended ;
and I shall use it only to signify the load in respect to which we
have, or intend to have, proof that it can be resisted by the
structure. The other meaning, which I reject, I would express in
such terms as the estimated extreme safe load ; and I would not
call that the proof load.

FACTORS OF SAFETY are of several kinds : — Thus, (1) A factor
of safety may be taken as the ratio in which the estimated
breaking or destructively damaging load exceeds the working load.
(2) Another factor of safety, having a different meaning, may be
the ratio in which the estimated breaking or destructively damag-
ing load exceeds the proof load. (3) Another factor of safety, and
that which most truly may be called a factor of safety, is the ratio
in which the proof load exceeds the working load.

The first of these factors is that to which the designer usually
gives his most special attention, because the destroying load is
the one as to which, for any material, we possess the most precise
information. He considers what is to be the working load for
which his structure must be designed. He then multiplies this
the number of times that he thinks the probable ultimate load
ought reasonably to exceed this working load ; and he then does
his best to design the structure so that it would just break or fail
at that ultimate load arrived at from the working load by his
factor of safety.

The ultimate load in any structure intended to be preserved
for use, must, of course, be only judged of by calculations, or
estimates from experiments on other like structures or on pieces
of the same kind of material tested up to their point of breakage,
or destructive alteration of form or of cohesion.

In respect to boilers, where the straining force is applied by
steam or water pressure, we may use the terms working pressure,
ultimate pressure, and proof pressure, which have an obvious
correspondence with the terms working load, ultimate load, and
proof load, already explained.

Now, in respect to boilers there is a prevailing opinion or
frequently adopted rule, to the effect that : —

1st, The ultimate strength of a good boiler should be at least
eight times that called into play under its working pressure.

That, 2nd, The proof pressure need not be more than twice the
working pressure, and that often less than twice is quite enough.

358 DYNAMICS AND ELASTICITY [53

And that, 3rd, The proof pressure ought not to be made more
than one-fourth of that corresponding to the ultimate strength of
the boiler.

The reason for keeping the proof so low as only twice, or less
than twice, the working pressure is fear of damaging the boiler.
That is, if the plain truth is to be spoken, fear that the ultimate
strength may probably be nothing like eight times the strength
called into play at the working pressure. If the fear were for
slight leakage alone, and for the consequent trouble and cost of
amending the defective parts, there would be some shadow of
justification for yielding to that fear; but what is usually said is,
that a severer test than about double the working load in the case
of a boiler whose calculated ultimate strength is eight times the
working load would tend to danger of bursting by its, perhaps,
overstraining and bulging some parts of the structure, and that
thus what would be meant for attaining safety against accidents
and loss of life would tend much more to the very opposite result.

In this view, when properly considered, there is to be found a
decided logical fallacy. It arises from a confusion between, on
the one hand, risk of injuring the usefulness of the boiler for
driving the engine and making money to its owner ; and, on the
other hand, risk of loss of life or limb to people whose lives or
limbs are staked on the sufficiency of the boiler, and risk of loss
of property to those whose goods may also be staked on its
sufficiency.

If there were any validity in the argument, it would go against
all proving beyond the working load; for in any new or in any old
boiler subjected to testing, some one part — a stay bar perhaps, or
an angle iron, or a gusset piece — may have an unseen flaw, or a
crack, or an unascertained quality of brittleness, and may be just
on the point of rupture under the very mild proof of double its
working load. Then, if the view I am combating were valid, this
defective part would be rendered more dangerous by the mild
proving. I say, however, in answer, that the proof ought rather
to have been made much more severe still, and then the defective
part would have been broken, or destructively altered, and so
would have been rendered powerless for causing future mischief by
its delusive estimated, but practically non-existent, strength rela-
tively to the duty to be imposed on it.

I say without hesitation that the greater the pressure that a

1873] SAFETY AND DANGER IN STRUCTURES 359

boiler has actually borne without bursting or leaking, the greater
will be its safety for the future ; and this the more so if the severe
test has been repeatedly applied without the occurrence of rupture
or destruction to any part. On the whole, my opinion is that
people, while liking to be left fondly to cherish the idea that
perhaps or probably they have a wide margin of extra strength for
the sake of security ; and while willing to pay for the material
required for such extra strengths, are habitually quite too
niggardly of making sure that they have a good margin at all.
Thus the material applied in giving strength that people will not
dare intentionally to call into play is really little better than waste
material in so far as any working within limits of safety is con-
cerned ; and beyond limits of safety people ought not willingly to
work their structures, or to allow them to be worked, when very
serious consequences would accompany the failure of the structures
in strength. Such extra material, no doubt, is a proper means
for diminishing the risk in unproved or insufficiently proved
structures; and it may often be properly introduced on that
ground, as also for affording greater durability against corrosion or
wear.

Cases no doubt may occur in which it may be better not to
prove a structure beyond the working load. Without waiting to
discuss such cases, I may suggest a bridge hastily constructed by
an army for its use in retreating before a pursuing enemy, or an
existing bridge of doubtful sufficiency which it is about to use in
the same circumstances; a worn rope let down a precipice for
escape of an unfortunate party of people surprised by a rising
tide ; the boiler of a merchant screw steamer pursued in time of
war by a privateer; or, on the other hand, the boiler of a privateer
pursued by a steam ship of war. In all these cases there is
danger both ways ; and then it may be wise to choose that which
seems the less.

Further, there are few engineers who have had much practical
concern with steam engines, and who cannot recall to mind cases
in which it has been preferred to continue working a boiler found
to be in very bad condition from age and corrosion, rather than
endanger the stoppage of some very important work, by venturing
to prove the boiler beyond its ordinary working load, and thereby
using means either to break it, or to remove all grounds of fear in
its use. On a tract of fen land, for instance, drained by steam

360 DYNAMICS AND ELASTICITY [53

power, the engine boiler was found to be very far gone, a new one
was ordered with all speed, the old one was kept working at forty
pounds to the square inch, but was not proved at all beyond this.
To have proved it even to forty-five pounds would have been
deemed to involve too much danger of breaking the boiler, causing
the stoppage of the engine, and the flooding of the low-lying
lands. This story is not an exact report of any one single
occurrence, but it is a fair representation of numerous cases often
occurring in the exigencies of the varied operations of men.

I have now been speaking of structures which would admit of
being proved beyond a definite working load which they are
required to resist. On the other hand, however, it is to be
observed that many structures, or most structures, indeed, from
their very nature do not admit of being proved experimentally,
but must be made and set to work on trust in the sufficiency of
the design and of the execution. A ship, as I have already
pointed out, is an instance of this kind ; and here, for due safety,
we have to rely on a large excess of calculated or estimated
strength in the various parts beyond that required in their
ordinary use, and in many of them beyond what may ever happen
to be called into exertion. We have also to submit in such cases
to have the clear knowledge that at best the structure is not
sufficient for resisting all the influences to which it may possibly
be exposed when in use, and that danger in its use cannot be
avoided.

Boilers, on the other hand, are a structure most peculiarly well
suited for perfect experimental testing. If two boilers executed
by different makers, but under the same specification and the
same terms of contract, and intended to work at 40 Ibs. to the
square inch, have their dimensions such that their calculated or
estimated bursting pressure will be 320 Ibs. to the square inch, or
eight times the working pressure, and if one be proved to 80 Ibs.
and the other to 120 Ibs., neither being found to fail, — surely the
one which has resisted 120 Ibs. will be more trustworthy, under
the various chances of possibly augmented pressure, through neg-
ligence or other causes, than the one which is only known to have
resisted 80 Ibs.

Though offering here for consideration a comparison of two
cases, in one of which the test is carried to twice, and in the other
to three times the working pressure; yet I do not wish to

1875] COMPARISONS OF SIMILAR STRUCTURES 361

pronounce upon any one particular margin for safety as that alone
which maybe proper in boilers in general or in bridges in general.
The decision as to what may be a suitable and proper margin to
require, or to provide, ought to depend on many circumstances in
individual cases; but I do wish to say that it is a great mistake to
assert a calculated strength of eight times the working load, while
at the same time admitting that three times or two and a half
times would be likely to cause damage.

The subject I have entered on, as to physical properties of
matter, and as to practices of men — as to what these practices are,
and as to what perhaps they ought to be, is a very wide one. I
might go on to say much respecting other structures, large and
small, besides those which I have already spoken of at some
length. I might proceed to discuss questions of safety and danger
in bridges, in water reservoirs, and in numerous small structures
in very common use ; and I might point out how, by testing and
proving, safety may be attained, or danger abated. I might point
out how, in some cases, multiplicity of parts tends to danger, as in
the numerous links of a chain, where any one being faulty destroys
the utility of all the rest ; and, on the other hand, how, through
multiplicity of parts, safety, almost perfect, is attainable without
testing in a wire cable. I cannot, however, attempt to exhaust
the subject, nor would I wish to exhaust your patience in this
introductory lecture. So I will now close, and leave any further
discussion of this and kindred subjects for future occasions.

54. COMPARISONS OF SIMILAR STRUCTURES AS TO ELASTICITY,
STRENGTH, AND STABILITY.

[From Transactions of the Institution of Engineers and Shipbuilders in
Scotland. 21st December, 1875.]

IN the brief considerations which I propose now to offer to
your attention, I do not know that there is anything to be
regarded in the light of a new discovery, or of an entirely new
'kind of investigation. I think, however, that I am able to bring
.together some easily intelligible and easily recollected principles,
which may often be of great practical use ; and that I can offer

362 DYNAMICS AND ELASTICITY [54

very simple and easy considerations for their establishment and
application.

The cases of similar structures which I propose to discuss are
of two kinds, very distinct, and which stand remarkably in contrast
each with the other.

I. The one relates to comparisons of similar structures in
respect to their elasticity and strength for resisting bending, or
damage, or breakage by similarly applied systems of forces.

II. The other relates to comparisons of similar structures as
to their stability, when that is mainly or essentially due to their
gravity*, or, as we may say, to the downward force which they
receive from gravitation.

For the first of the two kinds of cases just referred to, a
comprehensive but simple and easily intelligible principle, which
it is proposed now to establish and illustrate, may be stated as
follows : —

General Principle. — Similar structures, if strained similarly
within limits of elasticity from their forms when free from applied
forces, must have their systems of applied forces, similar in arrange-
ment and of amounts, at homologous places, proportional to the
squares of their homologous linear dimensions.

To establish this we have only to build up, in imagination,
both structures out of similar small elements or blocks, alike

* The word gravity is here preferred to weight, although the word weight has
been, and still is, very commonly used for conveying the meaning here intended
to be expressed. The common word weight has unfortunately two meanings in
frequent use, and this ambiguity is a troublesome source of perplexity in mechanics
and in other branches of Natural Philosophy. Firstly, the word " weight " very
commonly signifies quantity of matter, as when we speak of a hundred-weight of
iron, or of four pounds weight of mercury, or when, in an Act of Parliament (18th
and 19th of Victoria, chapter 72, July 30, 1855) for the special purpose of establish-
ing standard weights and measures, it is enacted that a certain piece of platinum
referred to as a " weight of platinum," deposited in the Office of the Exchequer,
shall be denominated the IMPERIAL STANDARD POUND AVOIRDUPOIS, and shall be
deemed to be the only standard of weight from which all other weights, and other
measures having reference to weight, shall be derived, computed, and ascertained.
And secondly, the same word "weight" is often used to signify the downward
force which a piece of matter exerts on whatever supports or suspends it ; as when
we speak of the weight of a piece of matter hung to a spring-balance as being the
force which draws out the spring. The word MASS is employed to express distinctly,
in scientific language, one of the two meanings of the word "weight" — that,
namely, in which it signifies quantity of matter ; but for the other meaning, in
which it signifies a force, we have no established name as yet ; it may, however,
very well be called the gravity of the piece of matter.

1875] COMPARISONS OF SIMILAR STRUCTURES 363

strained, with the same intensity and direction of stress in each
new pair of homologous elements built into the pair of objects.
(See figures below.) To aid our conception, we may first imagine
both structures to be free from forces applied to them from
without, and we may imagine the two to be similarly divided
into a great number of small similar elements, or blocks, similarly
situated. Thus we may notice that since the similar elementary

Fig. 1.

blocks, unstrained, would fit together in both cases, so as to
produce two similar unstrained structures, the blocks, or elements,
if alike stressed in homologous pairs in the two cases, so as to be
similarly deformed from their free condition, would also go together
so as to produce two similar structures similarly strained from
their free condition*.

* A case liable to occur in practice, but which is very commonly, and some-
times erroneously, neglected or left unnoticed in investigations on strength and
elasticity of materials and structures, is here, for simplicity, left out of consideration
— the case, namely, in which a piece of material, or a structure, is subject to
stresses in its substance, arising from mutual action of its parts when free from
externally applied forces. The principles discussed in the present paper are, how-
ever, easily applied to such cases, but, for avoidance of any extra complication,
the detailed discussion of such cases is not here entered on. It may suffice to say
that, so long as the utmost stresses do not strain any part of the substance of

364 DYNAMICS AND ELASTICITY [54

Now, if we confine attention for a moment to any pair of
homologous elementary blocks in the two structures, considering
them by themselves, and regarding the immediately adjoining
elementary blocks which meet them face to face as being objects
external to them, though not external to the entire structures, we
may observe, from the nature of the case, since the elementary
blocks are extremely small in comparison with the structures of
which they form parts, that each of them, in being strained, can
only be homogeneously strained and homogeneously stressed
throughout its body. We can then obviously see that if the two
are similarly strained from their forms when free, the strain* being
homogeneous throughout each of them, the two must be exerting,
out from themselves, at their homologous faces, stresses similarly
disposed, and equal in intensities, or proportional in total amounts
to the areas of those faces. Or, in other words, the homologous
faces of the pair of elementary blocks must be exerting out from
those blocks, on objects external to them, systems of forces
similarly disposed, and proportional in total amounts to the areas
of the element faces, or to the squares of homologous linear
dimensions of the two entire structures to which the single
elementary blocks of the pair respectively belong. Thus such
pairs of the elementary blocks as have homologous faces so situated
as to receive the action of the forces applied from sources external
to the entire structures, can only be exerting outwards against
these forces their own stresses already specified as being similarly
disposed, and proportional in total amounts to the squares of
homologous linear dimensions of the structures. Conversely we
see that the forces applied from without, subject to which the two
similar structures will be, at all homologous places, similarly

either structure beyond limits of elasticity, and provided that the ordinarily
existing condition of elasticity (known as Hooke's law), and which may be briefly
described as stress proportional to strain, or more precisely, as unital stress pro-
portional to unital strain, applies truly to the material of the structures, the
conclusions arrived at here as to the similarly applied forces and the similarity of
the strains and stresses produced by them, will be in no degree affected by the
antecedent existence or non-existence of internal stresses in the structures when
free from forces applied from without. In respect to this subject, reference may
be made to a paper by the author, published in the Cambridge and Dublin Mathe-
matical Journal, November, 1848, " On the Strength of Materials, as influenced by
the Existence or Non-Existence of certain Mutual Strains among the Particles
composing them." [See supra, p. 334.]

1875] COMPARISONS OF SIMILAR STRUCTURES 365

strained and stressed, must be similarly disposed and of amounts
at homologous places proportional to the squares of homologous
linear dimensions of the two structures.

From what has been now shown, we find that similar structures
of different dimensions must not be similarly loaded, that is to
say, must not be loaded with similar masses, if they are to be
stressed with equal severity, and are thus to undergo similar
deformations, or are to continue similar, each to other, after being
loaded. We see this because loads similar to the structures
would, if actually resisted, apply at homologous places forces
proportional to the cubes of homologous linear dimensions; but
the similarly deformed structures would exert on external objects
homologous forces proportional only to the squares of the homo-
logous linear dimensions ; and so, if the load in the smaller

structure were just such as to be balanced by the elastic forces
exerted by that structure, a similar load, if attempted to be
applied to the larger structure, would be too much for the elastic
forces exerted by that larger structure when similarly deformed so
as to be alike stressed, and so would not, in actual fact, be resisted
by the larger structure deformed similarly to the deformation of
the smaller.

The simple case of two similar wires with two similar weights
suspended (as in the accompanying figure), will illustrate this
general statement. The weights, and consequently the forces
which they apply, are as the cubes of the diameters of the wires ;
but the cross-sectional areas of the wires are only as the squares,
and so the unital stresses in the wires (that is to say, the stress-
rates per unit of area) are in the ratio of the linear dimensions,

366 DYNAMICS AND ELASTICITY [54

and are thus more severe in the larger structure than in the
smaller. This easy case is here selected for illustration of the
general principle applicable alike to simple and to complex cases,
because, from its extreme simplicity, its conditions can be perceived
without any elaborate reasoning ; while, by the agreement of the
results obviously exhibited in it with those announced in the
general statement, an easy illustration and verification of that
statement is afforded.

Numberless other examples or illustrations might be offered,
but a few will suffice.

We may consider the case of the comparison of two similar
girders or horizontal beams, rectangular in their cross sections
(like flooring joists), and each loaded only with its own weight ;
and we may suppose the similar forms and the dimensions to be
such that in neither case do the utmost stresses anywhere intro-
duced exceed the limit of elasticity of the material ; and that the
beams do not bend, in either case, to any such considerable
curvature as to vitiate importantly the application of the ordinary
formula which will be used.

For the elastic deflection of rectangular beams of uniform
cross section, and loaded uniformly along their length, while
placed horizontally and supported at both ends, we may use the
well-known formula, —

I denotes the length between supports,

b the breadth of the beam,

d its depth,

E the modulus of elasticity,

p the load applied, and

8 the deflection or depression at middle due to the load.

Now, putting u to denote any chosen homologous linear dimension
in the larger and smaller beam, we see that p oc us, I oc u, b oc u,
and d x u ; and hence from the formula we get

*

o oc

,
3

or o oc

uu

That is, the deflections of similar rectangular beams supported as
has been stated, and loaded with their own weights, would increase
proportionally to the squares of the linear dimensions. But,

1875] COMPARISONS OF SIMILAR STRUCTURES 367

obviously, for the production of equally severe stresses, the deflec-
tions ought to be proportional only to the linear dimensions, and
consequently the larger beam will be more severely stressed by the
load of its own weight than the smaller one will be in like manner
by the load of its own weight.

Again, as another example, let us suppose that a tank of boiler
plate, or of cast iron plates, for holding water, is arranged, for
simplicity, to stand on three columns placed triangularly on the
ground thus .'., so that the tank is supported simply at three
points of itself, and that it has been found of sufficient strength
for bearing the load of water which fills it; and let us suppose
that it is judged to be of good design, neither too strong nor too
weak. Let it be proposed to construct another tank like this one,
of exactly the same proportions in all respects, but having all its
linear dimensions exactly double of the corresponding linear
dimensions of the one already successfully in use. The question
arises, What inference is to be drawn, as to whether the proposed
larger tank would be of suitable strength, or needlessly too strong
or too weak, for bearing to be filled with water, from the informa-
tion that the similar, but smaller, tank is of just suitable and
proper strength for what it has to bear ? The answer, which in
this case would not be attainable in any such easy ways as were
available in the two very simple cases previously adduced, is
obtainable at once from the general principles which have been
demonstrated. Thus we see, in comparing the loads of water
pressure that can be borne on homologous areas in the smaller and
the larger tank, that in order to introduce equal intensities of
stress at corresponding places in the metal of both tanks, and
therefore to produce similar deformations in both, the loads of
water pressure on homologous areas must be proportional to the
squares of the linear dimensions ; or, in the case supposed, must
be four times as much in the larger tank as in the smaller, but
that the actual loads would be eight times as much in the larger
as in the smaller tank. Hence the larger tank would be insuffi-
cient in strength for its load, or would have a less margin of
superabundant strength for safety than the smaller one has.

Now, from the particular cases which have been adduced, and
from the general principles which have been demonstrated, we
may see that it would be wrong to judge from the sufficiency of
strength of a model beam bridge, or of a water tank or other

368 DYNAMICS AND ELASTICITY [54

structure, in circumstances such as have been under consideration,
that the larger corresponding structure would be likewise suffi-
cient. In fact, we may notice in general that, in order to have
similar structures to take similar deformations under the action of
loads of material similar to the structures and similarly disposed,
and to have equal margins of superabundant strength for safety,
it would be necessary that the specific rigidity and strength of
the material should increase directly in proportion to the homolo-
gous linear dimensions of the structures. But such is not the
case in fact; and so, as we go on enlarging our already large
structures (beam bridges or ships, for instance), if we^ keep
to the same proportions, we must come ultimately to dimensions
such that the structure will break down by its own gravity.

Referring now again to the general principle which has been
laid down and demonstrated in the early part of this paper — viz.,
That similar structures, if strained similarly within limits of
elasticity from their forms when free from applied forces, must
have their systems of applied forces similar in arrangement and
of amounts, at homologous places, proportional to the squares of
homologous linear dimensions — we may see that it affords very
tolerably satisfactory means of judging of the relation between
large and small similar structures which have to resist the forces
of wind, when those structures depend for their sufficiency mainly
on their strength, and their gravity does not come into account as
having any very important influence among the conditions affecting
the results. Thus, if we compare two similar masts carrying
similar sails, and being either with or without stay-ropes similar
in arrangement, and having their sails alike exposed to the wind —
so that we may assume as being at least approximately enough
true — that the force of the wind per unit of area is the same at
corresponding places in the two structures; or that, in other
words, on homologous areas in the two structures, the force of the
wind will be similarly applied as to direction, and will, in magni-
tude, be in the ratio of the squares of homologous linear dimensions,
we may judge that the two will be similarly strained, and will be
stressed with equal severity at all homologous places, and thus
that both will be alike suitable for resisting the force of the same
day's wind.

For the same reasons, it would appear that two umbrellas —
similar in form at every part, but different in size — would be alike

1875] COMPARISONS OF SIMILAR STRUCTURES 369

suitable for resisting the same kinds of exposure to the same
storminess of weather.

From the considerations already adduced, it is easy to pass on
to the consideration of strains beyond elastic limits, and to show
that in structures of similar forms, and composed of materials
exactly alike in qualities, at all homologous parts, we have a right
to expect the introduction of similar sets, or permanent changes of
form by similar systems of externally applied forces; and to expect
that similar deformations past elastic limits should bring the
smaller and the larger structure to the point of rupture together.

As an instance of what is comprised in this latter statement,
it may be noticed that, contrary to ideas very frequently enter-
tained, and which have sometimes affected decisions in important
practical cases, we ought to expect a thick boiler plate or plate for
shipbuilding, or a round or square iron bar, large in cross section,
to admit of being bent double cold without cracking, just as
readily as a thin plate or small similar bar of exactly the same
quality of material. People often take the view that in the
thicker plate or bar there must be more stretching of the outer
part at the bend than in the thinner plate or bar. It ought to be
recollected, however, that although in the larger one there be a
greater total stretching, yet there is in like proportion a greater
length of material to receive this greater stretching, and the
deformation of any homologous small elementary blocks in the two
will be exactly similar; or equal very small blocks similarly
situated in both will be alike deformed, and therefore equally
severely dealt with. Now, no doubt we are accustomed to find as
a matter of fact that thick bars or thick plates, which men can
make with their available means and appliances, do not admit of
bending in a ductile or malleable manner without breaking, as
well as thin bars or plates of good quality do ; but this is to be
attributed to the difficulty or impracticability of making large
forgings of qualities of material as good as are easily attainable in
thin plates or in bars of small cross section.

Passing now to the second class of cases of similar structures
referred to at the opening of the present paper — the class, namely,
which relates to comparisons of similar structures as to their
stability, when that is mainly or essentially due to their gravity
(commonly named as their weight) — we may see that, if we regard
the cases to be dealt with as being such that in them the strength

T. 24

370

DYNAMICS AND ELASTICITY

[54

of the material is amply sufficient to prevent the occurrence of any
such failure of strength at any part of either structure as would
be in any important degree influential on the relative stabilities
of the structures of different sizes, the similar structures will be
brought alike to be just ready to fail in stability (that is, alike
ready to be overturned) by the application on their surfaces of
similar force-systems, the magnitudes of the forces applied on
homologous areas being in the ratio of the cubes of homologous
linear dimensions of the different structures ; or, in other words,
the intensities of the forces applied at similarly situated places
being in the ratio of the homologous linear dimensions. ,

In reference to this, we may first consider the case of two
similar obelisks, or two similar pinnacles, supposing them to be
acted on by wind pressing on all corresponding patches of surface

A

CA

C'A'

Fig. 3.

of the two objects, similarly in direction, and with the same intensity
of force ; and we may suppose the material to have sufficient
strength to prevent the introduction of any important influence
on their relative stabilities, from crushing or failing of the material
in either case, at any place where it would become severely pressed
at the edge of the base round which rotation would occur if over-
turning were effected.

Obviously, the resultants of the forces of the wind, acting as
here supposed, on the two obelisks will be similarly situated, as
shown by R and R in the figure : and their magnitudes will be
as the squares of homologous linear dimensions ; and their arms or
leverages for their overturning moments round A and A' will be
as the linear dimensions. Hence the moments of the overturning

1875] COMPARISONS OF SIMILAR STRUCTURES 371

motives will be as the cubes of the linear dimensions. But if the
obelisks were both on the point of overturning, the resisting
moments would be as the fourth powers of the linear dimensions,
because the gravities of the two obelisks are as the cubes of the
linear dimensions, and the arms or leverages at which they act
round the edges A and A' are GA and C'A' respectively, which
obviously are as the linear dimensions. Thus we see that the
larger obelisk would resist a force of wind which would blow down
the smaller one; and we can readily see, further, that to make
both be just on the point of overturning by the action of similar
systems of forces applied by wind, the forces per unit of area at
corresponding places would be in the ratio of the linear dimen-
sions. If, for instance, one of them is of linear dimensions double
of those of the other, it will be able to bear twice as much force of
wind per square foot as the smaller one can bear ; it will be able
to bear eight times as much force on every element of its surface
as the smaller one can bear on every corresponding element of its
surface ; and, in the aggregate, the resultant of all the wind forces
which it will be able to bear will be eight times as great as the
resultant of all the wind forces which the smaller one can bear ;
and, further, the moment of the overturning motive, and that of
the equal and opposite resisting turning motive, will each be
sixteen times as great in the larger structure as in the smaller
one.

The consideration of the relations between factory chimneys or
other chimneys, similar in form but differing in dimensions, may
be aided, though not fully elucidated, by consideration, in connec-
tion with them, of the principles just adduced for the supposed
cases of obelisks and pinnacles. In the case of large chimneys,
the yielding of the material by crushing at the severely compressed
edge of the base, or by crushing, splitting, or otherwise lailing
through deficiency of strength at any part, would be decidedly
influential, and in some cases might be largely influential, on the
results, and therefore must not be left out of account in any very
complete consideration of the subject. In their case too, as also
in that of obelisks, standing with their bases at or near the ground,
we must bear in mind that the taller of any two structures, com-
paratively considered, will ordinarily be exposed to a greater force
of wind per square foot at any part of its surface than the lower
one would be exposed to at the corresponding part of its surface,

24—2

372 DYNAMICS AND ELASTICITY [55

because the velocity of the wind low down is more abated by
friction on the ground and by sheltering obstructions, such as
houses and trees, than at higher elevations. Still we may judge
with much confidence that the larger of two similar chimneys may
be expected to be capable of standing against a greater storm
than the smaller could endure ; and we may see that it would be
an unsafe procedure to judge, from the known sufficiency of a
large chimney, that a smaller one, constructed in the same propor-
tions as to general configuration, and of like material, would be of
sufficient stability.

[This subject was extended and developed by Professor Archibald Barr,
D.Sc., in a Paper ' Comparisons of Similar Structures and Machines ' read
before the Institution of Engineers and Shipbuilders in Scotland, 21st March,
1899. Volume XLII. page 322.]

55. ON METRIC UNITS OF FORCE, ENERGY, AND POWER, LARGER
THAN THOSE ON THE CENTIMETRE-GRAM-SECOND SYSTEM.

[From the Report of the British Association, Glasgow, Section A,
1876, p. 32.]

THE author premises that under the excellent method of Gauss
for establishing units of force, a unit of force is taken as being
the force which, if applied to a unit of mass for a unit of time,
will impart to it a unit of velocity. In the system already adopted
by the British Association Committee on Dynamical and Electrical
Units (Brit. Assoc. Report, part i. 1873, page 222), the Centimetre,
the Gram*, and the Second were taken as the units of length, of
mass, and of time ; and the unit of force thence derived under the
method of Gauss was called the Dyne.

That force is very small, quite too small for convenient use in
all ordinary mechanical or engineering investigations. It is about
equal to the gravity of a milligram mass, and that force is so
small that it cannot be felt when applied to the hand. That

* The spelling Gram, instead of Gramme, for the English word is adopted in
the present paper in accordance with the spelling put forward in the Metric
Weights and Measures Act, 1864, which legalizes the use of the Metric System
in Great Britain and Ireland.

1876] METRIC UNITS OF FORCE, ENERGY, AND POWER 373

system, designated as the Centimetre-Gram-Second System, re-
commended by the Committee of the British Association, and
described fully, with many applications, in a book since published
by Dr Everett, who was Secretary to the Committee, is well suited
for many dynamical and electrical purposes ; and it ought certainly
to be maintained for use in all cases in which it is convenient.
But the object of the present paper is to recommend the employ-
ment also of two other systems which are in perfect harmony with
it, and to propose names for the units of force under these two
systems.

In one of these systems, the Decimetre, the Kilogram, and the
Second are the units adopted for length, mass, and time ; and thus
the system comes to be called the Decimefcre-Kilogram-Second
System.

In the other, the Metre, the Tonne*, and the Second are
adopted as the units of length, mass, and time ; and thus the
system comes to be called the Metre-Tonne-Second System.

It is to be particularly observed that all the three systems
here referred to are framed so as to attain the condition, very
important for convenience, that the unit of mass adopted is the
mass of a unit volume of water, and that, therefore, for every
substance the specific gravity and the density, or mass per unit of
volume, are made to be numerically the same.

In the Decimetre-Kilogram-Second System, the unit of force
derived by the method of Gauss is 10,000 Dynes, or is about equal
to the gravity of 10 Grams. It is impossible, or almost so, to
work practically with any such system without having a name for
the unit of force. The unit of force in this system is such that
a human hair is well suited for bearing it as a pull, with ample
allowance of extra strength for safety against breakage ; and the
author proposes to call it the Crinal, from the Latin crinis and
crinalis.

In the Metre-Tonne-Second System the unit of force, likewise
derived by the Gaussian method, is 10,000 Crinals, or 100,000,000
Dynes, or is about equal to the gravity of 2 cwt., or of -^ of a ton.
This force would be properly borne as a pull by a moderately-sized
rope ; and the author proposes to call it the Funal, from the Latin
funis and funalis.

* The Tonne is the mass or quantity of matter contained in a cubic metre of
water, and is very nearly the same as the British Ton.

374 DYNAMICS AND ELASTICITY [55

Then we have One Horse-Power, of 33,000 foot-pounds per
minute, about equal to 75,000 Decimetre-Crinals per second ; and
the Horse-Power is also about equal to '75 of a Metre-Funal per
second.

Also 1 Metre-Funal

= 100,000 Decimetre-Crinals,
= 10,000,000,000 Centimetre-Dynes, or Ergs,
= 1010 Ergs.
Also 1 Horse-Power is about

= 7,500,000,000 Centimetre-Dynes per second, ^
or as the same may be written

75 x 108 Centimetre-Dynes per second.

The number 7,500,000,000, for expressing a Horse-Power under
the Centimetre-Gram-Second System, is an exceedingly unmanage-
able one ; and it gives a very decisive indication that the Centi-
metre and Gram are too small to be suitable as fundamental
units of length and of mass for ordinary engineering purposes ;
and that there is great need for the establishment of systems
having larger units, such as those which have been recommended
in the present paper, and for which a convenient nomenclature has
been offered.

It is to be observed that the provision made by the British
Association Committee, in the Report already referred to, of
a multiple of the Dyne, such as the Megadyne, or million of Dynes,
as a larger unit of force, does not accomplish all that is to be
desired, because various important formulas, or convenient methods
of statement, will not hold good when any of the units are so
derived. Thus, for instance, if the Megadyne be the unit of force,
while the Gram and Second are the units of mass and time, the
ordinary formulas for giving the so-called " centrifugal force " of
a revolving mass,

F = — and F = mtfr,

will not hold good ; and, as another instance, we may notice that
the proposition that, in respect to a jet of water, the reaction force
on the vessel is equal numerically to the momentum generated
per second, will not hold good; and numberless other instances
might readily be cited, but those given may suffice.

1878] DIMENSIONAL EQUATIONS, THEIR VERBAL EXPRESSION 375

56. ON DIMENSIONAL EQUATIONS, AND ON SOME VERBAL
EXPRESSIONS IN NUMERICAL SCIENCE.

[From the Report of the British Association, Section A, Dublin,
1878, p. 451.]

IN recent years attention has been given, more than before, to
relations among standard quantities of variable things, to be taken
as units for use in giving numerical expression to various quantities
of those things. The quantity of each different variable thing
selected as a unit might be, and often has been, arbitrarily chosen,
independently of the quantities chosen for units of other things.
But great advantages as to convenience and facility are attainable
by making a methodical connection among the quantities to be
selected for the units of the various things, so that when some of
the units are arbitrarily selected, the others will be derived from
them in some good systematic way.

The units thus arbitrarily selected are called fundamental
units ; and the others obtainable from them by the systematic
method are called derived units.

Teaching on this subject is given in the early pages of Professor
Clerk Maxwell's Treatise on Electricity and Magnetism, and in
Professor Everett's Treatise on the Centimetre-Gramme- Second
System of Units. The subject is important ; but much of the
nomenclature and notation hitherto used is very confusing and
unsatisfactory.

I now wish to propose some amendments, or new modes of
expression, which appear to be commendable.

Instead of saying, as is done in Professor Everett's ver^ useful
treatise,

" The unit of acceleration varies directly as the unit of length,
and inversely as the square of the unit of time ; "
I would propose to say

The change-ratio of the unit of acceleration is the product of
the change-ratio of the unit of length and the inverse second power
of the change-ratio of the unit of time.

The meaning of the new name, change-ratio, may be given by
the following definition.

376 DYNAMICS AND ELASTICITY [56

DEFINITION. — In respect to changes of any variable, the change-
ratio is the ratio of the new value to the old, for any change from
one value of that variable to another.

Further, in Everett's treatise, the relation already referred to
among the units of length, time, and acceleration, is stated in some
other ways, which I will next cite : —

" The dimensions of acceleration are , . .„ .'

(time)2

" The dimensions of the unit of acceleration are

unit of length „ ^

(unit of time)2'

Instead of either of these, I would substitute this —
Change-ratio of unit of acceleration

_ change-ratio of unit of length
(change-ratio of unit of time)2'

This expression states clearly and correctly all the truth which is
meant to be conveyed by the previous statements.

In order now to be enabled to speak, in language brief and free
from ambiguity, of any numerical expression whatever, whether
whole or fractional, greater or less than unity, or unity itself,
I shall use the word numeric, which I recommend for general use,
to comprise all the meanings which at present are conveyed in
common use, but with much of troublesome ambiguity, by words
or phrases such as number, fraction, number or fraction, number
and fraction, number or proper fraction or improper fraction.
I recommend that, as soon as possible, the word number should be
restricted to its only proper signification, which is often at present
designated in an objectionable way by the two words "whole
number" but which is often also expressed, and really properly so,
by the single word number*.

* Thus, for instance, in the public regulations for Post Office Savings Banks,
issued by authority of the Postmaster-General (British Postal Guide), the intima-
tion is made that "At these banks deposits of one shilling, or any number of shillings,
will be received," this being, however, subject to some restrictions, which need not
be mentioned here, merely assigning limits to the amounts that will be accepted
from any one person. Now the words here quoted would convey a false statement
of what the Post Office authorities really mean to announce, if the word " number "
were allowed to mean a fractional numerical expression. The announcement is
obviously framed on the assumption that the word "number" in it can only mean
legally what in the present paper is referred to as its only proper signification,

1878] DIMENSIONAL EQUATIONS, THEIR VERBAL EXPRESSION 377

Now we have no right to speak of dividing one quantity by
another of a dissimilar kind, except, merely for brevity, in the case
of dividing the numeric expressing the one quantity by the
numeric expressing the other quantity, after we have fixed upon
units of the two things. Thus we have no right to speak of unit
of length divided by unit of time, nor to employ, unless perhaps
for brevity, and under an implied protest, such a notation as

Unit of length
Unit of time

Further, we have no right to speak of " second power of unit of
time!' nor of "square of unit of time." The name power seems
admirably well suited (whether by deliberate design entirely, or
partly by good chances) for its uses in reference to what are called
powers, whether integral or fractional, of any numerics, as for
instance

x2, a;3, a£, #2'13, &c., &c.;

and also for its uses in cases such as

#~2, a?"3, #~2, #~2'13, &c., &c.;

in any of which x may denote any numeric whole or fractional.

Such expressions as the square of the unit of time are not to be
approved of. That expression, for instance, is too like such
combinations of words as a square second, or a square minute. It
is not really quite so unreasonable, however, because there is
a good meaning sometimes intended though badly expressed, when
the square of the unit of time is spoken of, that unit being then
regarded as a variable, and the true meaning being usually just
what may be distinctly stated as the second power of the change-
ratio of the unit of time. A second is essentially a constant
quantity of time ; and the square of a second, a second squared,
and the second power of a second of time, are all of them essentially
meaningless conjunctions of words.

that, namely, which is commonly designated as "a whole number" or " an integer."
If an intending depositor, understanding the word "number" in the extended sense
in which it is very often, and also quite authoritatively used, would offer a deposit
of 7£a., his offer would be refused, as it would amount to 7s. 4d., which is not
contemplated in the regulations as an amount to be accepted as a deposit.

More examples to the same effect might be cited from usages in practical
business affairs ; and also from usages of scientific writers in arithmetic, and in
other branches of mathematics, but the one here given may suffice.

378 DYNAMICS AND ELASTICITY [56

It is to be observed that any ratio is a numeric, or may be
treated as such to any degree of approximation we please ; and so
we can have the second power or any other power of a change-
ratio ; and we are entitled properly to write as a fraction any power
of any change-ratio divided by any power of the same or of any
other change-ratio. That fraction will be itself a numeric, and
may properly form one side of an equation having a numeric for
its other side.

It follows, then, under the views already offered, as to
legitimate and illegitimate modes of expression and notation, that
such notations as A

yard 1 foot

(minute)2 ~ 1200 (second)2 '

which is given in Dr Everett's Treatise (page 4), as a very ex-
pressive notation now becoming common, are not commendable,
and are such as it is desirable promptly to reject. We might quite
rightly note that

yard 1 /minutey

foot = 1200 ( second J '

but it would be illegitimate to pass from this, by imitation of
a real algebraic process, so as to write

yard 1 (minute)2
foot = 1200 (second)2 '

and thence further to make a pseudo-multiplication of both sides
by foot, and a pseudo-division of both sides by (minute)2, and so to
bring out the seeming equation above objected to.

The name dimensions of units is subject to a distressing
ambiguity. It might mean the greatness or smallness of them ;
and indeed a dimensional equation is for the very purpose of telling
how the greatness of some units changes in accordance with changes
made in the greatness of other units. This is not, however, the
idea which is attached to the word dimensions in dimensional
equations. It is mentally associated rather with such notions as
the three dimensions in space, length, breadth, and thickness (not
to say also with the fanciful notions, so often now put forward, of
a fourth dimension in space, or a 2Jth, or 4|th, or an infinite
number of other alleged dimensions in a dreamland space, not
found in our world or conceived in our brain). It has, in fact, to
do with change-ratios, or powers of change-ratios of quantitative

1884] INERTIA: CHRONOMETRY: ABSOLUTE MOTION 379

units, whereby the magnitudes of the various units are mutually
connected, and some of them specified by reference to others.
There is, I may remark, for instance, in Dr Everett's book, one
article on Dimensions of Units, and another on Dimensions of the
Earth. Now the word dimensions in these two cases has totally
different meanings.

57. ON THE LAW OF INERTIA; THE PRINCIPLE OF CHRONO-
METRY; AND THE PRINCIPLE OF ABSOLUTE CLINURAL REST,
AND OF ABSOLUTE ROTATION.

[From the Proceedings of the Royal Society of Edinburgh, 3rd March 1884,

Vol. xn, p. 568.]

THERE is no distinction known to men among states of existence
of a body which can give reason for any one state being regarded
as a state of absolute rest in space, and any other being regarded
as a state of uniform rectilinear motion. Men have no means of
knowing, nor even of imagining, any one length rather than any
other, as being the distance between the place occupied by the
centre of a ball at present, and the place that was occupied by
that centre at any past instant ; nor of knowing or imagining any
one direction, rather than any other, as being the direction of the
straight line from the former place to the new place, if the ball is
supposed to have been moving in space. The point of space that
was occupied by the centre of the ball at any specified past moment
is utterly lost to us as soon as that moment is past, or as soon as
the centre has moved out of that point, having left no trace
recognisable by us of its past place in the universe of space.

There is then an essential difficulty as to our forming a distinct
conception either of rest or of rectilinear motion through unmarked
space.

We have besides no preliminary knowledge of any principle
of chronometry, and for this additional reason we are under an
essential preliminary difficulty as to attaching any clear meaning
to the words uniform rectilinear motion as commonly employed,
the uniformity being that of equality of spaces passed over in
equal times.

If two balls are altering their distance apart, we cannot suppose
that they are both at rest. One, at. least, must be in motion.

380 DYNAMICS AND ELASTICITY [57

Men have very good means of knowing in some cases, and of
imagining in other cases, the distance between the points of space
simultaneously occupied by the centres of two balls ; if, at least, we
be content to waive the difficulty as to imperfection of our means
of ascertaining or specifying, or clearly idealising, simultaneity at
distant places. For this we do commonly use signals by sound,
by light, by electricity, by connecting wires or bars, and by various
other means. The time required in the transmission of the
signal involves an imperfection in human powers of ascertaining
simultaneity of occurrences in distant places. It seems, however,
probably not to involve any difficulty of idealising or imagining
the existence of simultaneity. Probably it may not be felt to
involve any difficulty comparable to that of attempting to form
a distinct notion of identity of place at successive times in un-
marked space.

There is, in the nature of things, a real distinction, cognisable
by men, between absolute rotation (or absolute clinural motion)
and absolute freedom from rotation (or absolute clinural rest)*.

The only motion of a point that men can know of or can deal
with is motion relative to one, two, three, or more other points.
Three points marked or indicated on one, two, or three bodies,
the centres, for instance, of three balls, whether preserving their
distances apart unchanging or not, are sufficient for enabling us
to construct or to imagine a reference frame of any changeless
configuration desired — three rectangular co-ordinate axes, for
instance, or three rectangular co-ordinate planes — to which the
situations, instantaneous or successive, of points may be referred.

Any arrangement whatever of points, lines, or planes, changeless
in mutual configuration, will, for present purposes, be named as a
reference frame, or briefly as a frame.

The word motion, in ordinary usages, has several varied signi-
ficances.

1. Thus it is often said that a body, or rather some specified
point of it, has performed a motion from a point A to a point B,
along a straight or curved line of motion A MB. It may be often

* The word clinural is to be understood as introduced for conveying precisely
one out of the various conflicting meanings of the word directional. All straight
lines which are mutually parallel are, in this amended mode of nomenclature, said
to be in one same clinure. In connection with this, it may be convenient here
to mention that all parallel planes are, in like manner, said to be in one same
posure.

1884] INERTIA: CHRONOMETRY: ABSOLUTE MOTION 381

said that this same motion has been effected slowly on one
occasion and quickly on another, speed or velocity of the moving
point not being treated as any essential quality or condition of
the motion.

Fig. 1.

2. Again, it is often said that a point, moving along a curve
GABH, has a certain motion at the instant of its passing A, and
that its motion 'undergoes change during the passage from A to B,
and that at B it has a motion changed from that which it had at
A. In this sense the motion at A is regarded as determined by
the line of motion specified as being the tangent to the curve at

Fig. 2.

A, and the ward, or way, of the motion along its line at the point
of contact A, and the velocity of the motion at that point. The
velocity of the motion is usually understood as meaning a true
time rate of motion — a rate which may be specified, for instance,
as being that of so many feet per second, or the like. For this
ordinary mode of specifying that which is to be called velocity, it
is necessary that true chronometry should have been previously
attained to, in idea at least, and approximately in fact.

Sometimes it is found convenient to apply, temporarily at
least, the name velocity (for want of any other name) to the rate
of travel of a point along a line as referred to the progress of
something else moving relatively to a frame or to a dial. Thus,
for a point moving along a line, the motion at any point of the
path may sometimes be said to have a velocity of so many feet
per unit of angular space turned by the crank shaft of a steam
engine relatively to the framing of the steam engine. What is
thus specified might be called a quasi-velocity ', not a true velocity,

382 DYNAMICS AND ELASTICITY [57

as it is customary to regard true velocity as being referred not to
the revolution of a steam engine shaft, nor to the revolution of
a hand of a badly-going clock, but to the progress of absolutely
true time when once the idea of progress of true time has been
arrived at.

Before arriving at any principle of absolute chronometry, how-
ever, we cannot deal with true velocity at all. We cannot specify
a rate of progress of any moving point relatively to progress of
true time, or relatively to progress of a clock hand on its dial
advancing proportionally to progress of true time. But, without
assuming or presupposing any principle of absolute chronornetry,
we can refer motions of points to an assumed reference frame,
jointly with an assumed dial-traveller. The dial-traveller may
conveniently be imagined as a clock hand or index travelling
continuously along a graduated dial, such as the face of a clock,
but without the adaptation of any pendulum or balance wheel, or
other chronometric arrangement for regulating the motion of the
hand. The traveller, for instance, might be kept moving round
its dial by a winch handle, such as that of a grindstone, or of
a barrel organ, turned by hand. Or it might be an index pro-
jecting out radially from the crank shaft of a steam engine, and
revolving round a dial fixed to the adjacent framework of the
engine, so as to surround the shaft. Or the traveller might be
an index kept revolving by the shaft of a water wheel, with a
motion depending on variable conditions of rain-fall and stream-
flow.

For purely kinematic considerations as to relative motions of
points or bodies we have no essential concern with true time, nor
with true velocities, understood as velocities of motions relative to
a frame, and specified quantitatively as true time rates.

Now, reverting to the essential difficulty already mentioned as
to our forming a distinct conception either of rest or of uniform
rectilinear motion, we may go forward to some further considera-
tions and scrutinies as to what men can imagine or can really
know, through observation and experience, respecting motions of
bodies in the universe of space.

We may have a firm persuasion, even without perfect under-
standing, that in the nature of things there must be a reality
corresponding to our glimmering idea of motion of a body along
a straight course with changeless velocity, and that there must be

1884] INERTIA: CHRONOMETRY: ABSOLUTE MOTION 383

an essential distinction between such motion and motion along
a curved course or motion with varying velocity. We cannot,
however, specify such motions relatively to unmarked space and
unmeasured passage of time. We cannot specify them as to any
condition of absolute rest. We can only specify them as to part
of their characters, or conditions, or distinctions. We can do so
only in so far as qualities or distinctions of motions of one or more
bodies can be ascertained through knowable relations between
these motions and the motions of one or more other bodies.
Briefly, we can deal only with relative motions or relative rest;
not with absolute motions nor absolute rest.

Sir Isaac Newton sets forth, under the designation of the
FIRST LAW OF MOTION, the statement that — Every body continues
in its state of resting or of moving uniformly in a straight coarse,
except in so much as, by applied forces, it is compelled to change
that state.

A most important truth in the nature of things, perceived

with more or less clearness, is at the root of this enunciation, but

the words, whether taken by themselves or in connection with

Newton's prefatory and accompanying definitions and illustrations,

are inadequate to give expression to that great natural truth.

In attempting to draw from the statement a perfectly intelligible

conception, we find ourselves confronted with the preliminary

difficulty or impossibility as to forming any perfectly distinct

notion of a meaning in respect to a single body, for the phrase

" state of resting or of moving uniformly in a straight course!'

Newton's previous assertion that there exists absolute space which,

in its own nature, without reference to anything else, always remains

alike and immovable, does not clear away the difficulty. It does

not do so, because it involves in itself the whole difficulty of our

inability to form a distinct notion of identical points or places in

unmarked space at successive times, or of our inability to conceive

any means whatever of recognising afterwards in any one point of

space, rather than in any other, the point of space which, at a

particular moment of past time, was occupied by a specified point

of a known body.

To aid in the apprehension of the underlying truth referred to,
and also as an aid to the understanding of the enunciation about
to be given in the present paper as The Law of Inertia and
Principle of Chronometry, some purely kinematic principles will

384 DYNAMICS AND ELASTICITY [57

now be adduced for consideration. Thus the question is to be
opened up as to what may be the nature of relative motions of
various bodies, which can in any sense truly be regarded as
uniform rectilinear mutual motions. Explanations are to be
given on such motions of points in unmarked space, as can have a
reference frame and reference dial-traveller relatively to which
jointly those motions are rectilinear and are uniform in the
sense of being changeless in quasi-velocity. In other words, quite
to the same effect — Explanations are to be given on such motions
of points in unmarked space as can have a reference frame relatively
to which those motions are rectilinear and are changeless in mutual
rate; or what is the same, are mutually proportional in their
simultaneous progress.

Let us imagine a reference frame, rigid in its configuration,
and for simplicity let it be taken as including three rectangular
reference planes firmly connected. Let several points or small
bodies be kept moving by geared mechanism, such as that of
toothed wheels on variously inclined axles, and toothed straight
sliding racks with pinions, all carried or guided in bearings firmly
attached to the reference frame, the arrangements being such
that those moving points shall be made simultaneously to travel
over mutually proportional lengths along straight lines fixed in
relation to the reference frame. The motion may be given by
a winch handle like that of a barrel organ, fixed on one of the
axles; and, for help in consideration of the subject, we may
imagine a uniformly graduated dial surrounding the winch handle
axle, and an index attached to the axle so as to project radially
outwards like a hand of a clock, and to travel round the dial
keeping pace in angular motion with the winch handle. Thus
the simultaneous travels of the various small bodies along their
straight courses are to be mutually proportional, and they are also
to be proportional each of them to the simultaneous travel of the
index on the dial. Now, if any other frame of three co-ordinate
planes be arranged to exist with the point of their intersection
keeping at any one of the moving points, and with the three
planes maintaining changeless angles with the original three
reference planes, any one of the moving points will either be at
rest relatively to the new set of reference planes, or will generate,
in relation to them, a straight line, and the simultaneous lengths
traversed by the various points relatively to these new reference

1884] INERTIA: CHRONOMETRY: ABSOLUTE MOTION 385

planes will be mutually proportional. It is convenient to notice,
in preparation for subsequent reference of motions to true time or
to a truly chronometric clock, that the simultaneous lengths
traversed by the various points relatively to the new reference
planes, and of the winch handle index relatively to its dial, will be
mutually proportional. We may thus see that for the established
set of motions of the points, there can exist as many sets of
reference planes or frames as we please, differently moving and
differently inclined, in reference to each of which every one of the
points will generate a straight line with a quasi-velocity (or rate
per dial-traveller progress) proportional to the quasi-velocity of
every other along its own line. We are now perfectly entitled to
speak of the motions of all these points as referred to any one of
the frames and the original dial-traveller, as being uniform recti-
linear motions. The word uniform, it should be noticed, has,
neither in its origin nor in its customary employment, any essential
connection with progress of time. The notion besides of the dial-
traveller as a standard to which the simultaneous travels of the
various points may conveniently be referred, or rated, is not at all
essential. We would be quite entitled, without knowledge of
chronometry, and without having recourse to the quasi-time
indicated by the dial-traveller, to speak of the motions of all the
points relatively to all the reference frames, as being uniform
rectilinear motions. The uniformity in rate of progress would be
in respect to rate of travel of any one of the points per simultaneous
travel of any other one of them. In all that has been said in this
matter no assumption has been made as to any particular condition
of rest or motion having belonged to the original reference frame.
It may have been firmly attached to the surface of the earth, or it
may have been firmly attached to the floor and side walls of the
cabin of a ship sailing in devious courses over the sea and tossing
on the waves. Notwithstanding any such motions, or any motions
whatever, belonging to the original reference frame, the mutual
motions of the points will possess the character that they admit of
having reference frames, as many as we please, relative to which
they will be rectilinear and mutually proportional (or, in other
words, they will be uniform rectilinear motions, by mutual
reference without reference to time). If the moving points alone
were available to us for progressive observation or measurement
it might be a difficult, perhaps an extremely difficult, geometrical
T. 25

386 DYNAMICS AND ELASTICITY [57

or kinematical problem* to find from them a reference frame
accomplishing the stated condition; but this does not hinder us
from easily and distinctly understanding that such a frame is
geometrically or kinematically possible. On the other hand, for
a set of points moving at random like flies in the air, or for a set
of points having uniform rectilinear motion as already described,
together with others revolving like satellites round some of them,
no reference frame to accomplish the conditions stated would be
possible. For a single fly moving anyhow, reference frames would
be possible, relative to any one of which the motion of the fly
would be rectilinear, and would be uniform in rate of progress
relatively to true time, or to any assumed standard whatever for
rate of progress ; but for two flies, or any greater number, no such
frame would be possible. Reasons for this are so obvious as
scarcely to require statement. Briefly, however, it may be men-
tioned that any two flies might in their mutual motions come
into contact once and then separate, and then come into contact
again; but no second meeting could occur with points moving
straightly and mutually proportionally in relation to any frame
whatever. Or the two flies might be increasing their distance
apart and afterwards diminishing it ; but no approach after reces-
sion is possible for points moving straightly and proportionally in
relation to any frame whatever.

The explanations now given are sufficient to show that there
can be mutual motions of various bodies, so related as to have a
property of being uniform rectilinear mutual motions, and to explain
the nature of that mutual relation. This is quite irrespective
of any idea of chronometry, or any idea of absolute rest or motion
in the universe, or of any idea of absolute clinural rest or absolute
rotation, and of any distinction whereby one body might be said
to be in absolute rotation and another devoid of absolute rotation.
The mutual relation described has been purely kinematic, and will

* Postscript Note, May 1884. — On the evening of the reading of the paper
(March 3, 1884), just after the close of the meeting of the Society, the author
inquired of Professor Tait whether he could see how the problem referred to here
in the paper as being perhaps extremely difficult, could be solved. Professor Tait
replied that he could solve it very briefly by use of quaternions. The author, not
being at all acquainted with quaternions, has since seen his way clearly to the
solution by an easy method of mechanical adaptations. The mechanical method is
merely for intellectual use, not for practical application. The ideal mechanism can
serve as an instrument for use in reasoning, though friction, and elasticity of materials,
&c., might render it incapable of complete practical realisation. [Of. infra, p. 401.]

1884] INERTIA : CHRONOMETRY : ABSOLUTE MOTION 387

not be at all altered by the superposition of any new motion
whether of translation or of rotation, the meaning of this state-
ment being rendered intelligible by consideration of the attachment
of the original reference frame to the floor and side walls of the
cabin of a ship at sea, already mentioned.

Now, to pass from mere geometric or kinematic motions,
governed mutually by connecting mechanism to the motions of
bodies existing in space free from any such governance, we are to
accept as an established law of nature, established through multi-
tudinous observations and speculations, together with theories
confirmed by multitudinous agreements, the following, which may
be called the law of inertia.

The Law of Inertia.

For any set of bodies acted on each by any force, a REFERENCE
FRAME and a REFERENCE DIAL-TRAVELLER are kinematically
possible, such that relatively to them conjointly, the motion of
the mass-centre of each body, undergoes change simultaneously
with any infinitely snort element of the dial-traveller progress,
or with any element during which the force on the body does not
alter in direction nor in magnitude, which change is proportional
to the intensity of the force acting on that body, and to the
simultaneous progress of the dial-traveller, and is made in the
direction of the force.

Principle of Chronometry.

From the foregoing law it is readily deducible, as a corollary
by elementary mathematical considerations, that —

Any dial- traveller which would accomplish the conditions
stated would make progress proportionally with any other dial-
traveller, obtained likewise from the same set of bodies, or any
other set of bodies with the same or any other reference frame.
Then, in view of this remarkable agreement, we define as being
equal intervals of time, or we assume as being somehow in their
own nature intrinsically and necessarily equal intervals of time,
the intervals during which any such dial-traveller passes over
equal spaces on its dial. Thus, any dial-traveller which would
accomplish the conditions stated would constitute a perfect
chronometer.

25—2

388 DYNAMICS AND ELASTICITY [57

This gives us the ideal of a perfect chronometer. It remains
for men to aim at approaching as near as they can towards that
ideal in the practical realisation of good chronometry.

For good and long-enduring realisations of chronometry, astro-
nomical methods are alone available. None of these present any
simple method of procedure. They require hypothetical assump-
tions of supposed forces acting on the bodies considered, and,
above all, there is involved in them the assumption, and after
multitudinous tests, accompanied by multitudinous confirmations,
the discovery of the Law of Universal Gravitational Attraction —
the grandest of the discoveries of Sir Isaac Newton. *

Principle of Absolute Clinural Rest and of Absolute Rotation.

Any straight line fixed relatively to any reference frame which
accomplishes the conditions specified in the statement of the law
of inertia has absolute clinural rest. If another straight line
fixed in any other such reference frame be parallel to that former
line, the two lines will continue parallel, so that by either of them
the one same absolute clinure is permanently preserved. The
principle here called that of absolute clinural rest is clearly
enunciated in Thomson and Tait's Natural Philosophy, § 249,
under the designation of "Directional Fixedness." It is there
exhibited by a very simple device, and here by a somewhat
different method.

Any body which has no rotation relative to a framing which
accomplishes the conditions stated is devoid of absolute rotation,
and if a body rotates relatively to any such frame it has the same
rotation absolutely.

The Law of Inertia here enunciated sets forth all the truth
which is either explicitly stated or is suggested by the First and
Second Laws in Sir Isaac Newton's arrangement.

By applying the Law of Inertia to the case in which the
forces acting on the bodies vanish, the law becomes a remodelled
substitute for the statement set forth by Sir Isaac Newton as the
First Law of Motion in his arrangement.

1884] REDUCTION OF MOTION TO SIMPLEST REFERENCE FRAME 389

58. A PROBLEM ON POINT-MOTIONS FOR WHICH A REFERENCE-
FRAME CAN SO EXIST AS TO HAVE THE MOTIONS OF THE

POINTS, RELATIVE TO IT, RECTILINEAR AND MUTUALLY
PROPORTIONAL.

[From the Proceedings of the Royal Society of Edinburgh, 7th July, 1884]

IN a paper read in this Society on the 3rd of March last*,
" On the Law of Inertia," &c., I had occasion to adduce for con-
sideration a problem to the following effect : —

Relatively to the reference-frame which may itself have any
motion whatever (but which is to be regarded as unknown or as
disallowed for any use in observation or measurement), a set of
points are known to have motions which are rectilinear and
mutually proportional in simultaneous progress. From observa-
tions or measurements on successive simultaneous configurations
of the set of points merely, to find a reference-frame relatively to
which their motions will have that same character.

On the suggestion of this problem for solution being made to
Prof. Tait, on the evening of the meeting already referred to, he
promptly replied that he could solve it very briefly by quaternions.
[See ante, page 386, footnote.] I myself soon after succeeded in
devising a solution, and my object in the present paper is to offer
that solution to the Society. Prof. Tait too, I trust will submit
his quaternion solution this evening to the Society.

Let us take the case of three points moving rectilinearly and
mutuo-proportionally relatively to a frame. Three points are
enough, but we might use more, and might so bring out varied
solutions; and besides it maybe mentioned here that a distinction
of importance will be found to exist between the results attainable
for three points only, and for a greater number than three. This
will be referred to at a later stage [near the end of the paper,
pages 399 and 400].

Let these three points to be used be called in general, A, B,
and C, irrespectively of changes in their mutual configuration, or
in their situations relative to any frame. Let us proceed to find
a frame relatively to which any one of these three points, say the

* [See supra, p. 379.]

390 DYNAMICS AND ELASTICITY [58

point C, shall be at rest, and the other two shall move rectilinearly
and mutuo-proportionally. Let successive simultaneous situations
of A and B at instants of measurements be designated as Al and
Blt A 2 and B2, As and B3, &c. We may thus bring into considera-
tion and into use a sort of portable triangles A-ffB^ A2GB2)
ASCB3, and more if wanted, representing severally in forms and
dimensions the likewise designated original triangles ; or, it may
be, representing the originals in form, while constructed on any
convenient scale of dimensions. The use of such altered scale is
to be understood as available if the full original sizes would be
inconvenient for use in a kinematical diagram, or mechanism, soon
to be explained for construction or ideal contemplation. After
this mere mention of allowable change of scale, the explanations
will generally be given, for brevity and simplicity, as if the
lengths of lines in the diagram, model, or mechanism, were
identical with those of the corresponding original lines, rather
than on an altered scale. We may denominate these several
portable triangles in succession as templet 1, templet 2, &c.

Let us take the corners C of the three templets together, and
take any plane passing through C, and bring the three lines GAl}
GA2) CAB, into that plane. Then take a straight line to be called
A A, movable in that plane; and, by motions of the lines CAl}
GA2, CA3, together with the motion of the line A A itself if
necessary, bring the templet points Alt A2) As, into the line A A.
Keep, until further notice, the line A A. at a constant distance
from G. This last bondage temporarily applied (that of keeping
A A at a constant distance from C) is introduced merely as an aid
in the reckoning of freedoms, and of their successive abolitions.
It is not essential, and for some possible varied modes of thought
it may well be omitted.

The figure here illustrates the arrangement so effected. It is
to be understood that we are to suppose ourselves free from any
doubt as to whether, at the instant of any measurement, the
moving point A or B, as the case may be, is diminishing or
increasing its distance from G; for instance, we are to suppose
that we are fully aware at which side of M in the line A A we are
to place the point Al', the line CM being the line of shortest
distance from G to A A.

Next take another straight line to be denominated as BB, and
place it passing through B-^ and B2 wherever these templet points

1884] REDUCTION OF MOTION TO SIMPLEST REFERENCE FRAME 391

may happen to be. Then rotate templet ASGB3 round its side
CA 3 till its side CBS) regarded as an interminate straight line,
comes to meet the line BB which itself is movable, and may, if
necessary or desirable, be shifted while retaining the points Bl
and J52 in it. This operation may be stated in other words as
being the operation of bringing the templet line CB3 into the
plane of B^ and B2 and C, or, what is the same, into the plane of
the point C and the line BB holding in it the points B1 and Bz.
Now, in general, on the accomplishment of this, we shall have the
three points Bl} B2, and B3, not in one straight line, though all in
the plane of B1} Bz, and C. That is to say, the line BiB2 will cut
the interminate line GB3, but generally not in its point Bs. But
now, rotate templet 1 round GA1 or templet 2 round OAZ till B9

Fig. l.

kept in the plane B1GB2 comes into the interminate straight line
J?!J52, or, what is the same, into the line BB. So now we have
attained to the following state of things, videlicet : —

Firstly. Line A A is kept at an unchangeable distance from
the point C.

Secondly. Three templet points A1} A2) As, are kept in the
straight line A A ; and three other templet points Blt B2) B3, are
all situated in one straight line BB.

Under these conditions, without departing from them, and
while considering the point C and the line A A, and consequently
CAly CA», CA3, as being all. at rest, we can move any one of the
three templets by rotation round its line GA ; and the other two
will be bound to move with that one, and to assume fixed places

392 DYNAMICS AND ELASTICITY [58

when that one is fixed ; — or, in other words, motion or rest of all
the three is exactly decided by motion or rest of any one templet.

Two VARIED METHODS FOR CONTINUATION.

Having arrived at this stage, we may go forward to accomplish
a solution by either of two branch methods which will be stated
now successively.

METHOD I. — The state ' of things already arrived at being
maintained, if now further we introduce one more templet A^GB^,
placing its point C to coincide with the C of the previous templets,
and bringing its point A4 into the line A A ; and if we rotate this
new templet round the fixed side CA 4 as an axis, and move also,
if we please, or if necessary, the line BB in the freedom it has,
and carry on either or both of such motions till we get the inter-
minate line CB4 to meet the interminate line BB (that is, in other
words, till we get CB4 into the plane of G and BB) the point B4
will not in general find itself in the line BB (but BB will meet
some point of CB4 other than B4). Let us, however, while
maintaining the arrangements or conditions already arrived at,
shift the line BB in the freedom it possesses till B4 comes into
that line BB, and then let us make that conjuncture binding for
the future.

Now all will be clamped or locked completely during our
maintenance of the temporarily employed condition of A A being
kept at an unchanging distance from G.

Next release that condition and shift A A to any new distance
from (7, and it will follow that BB will be fixed in a new situation;
and, for A A moving, BB will be bound to an exact movement
accordingly.

But now introduce one more of the templets, templet A5CB5)
with its point A5 brought into the line A A and kept bound to
remain in that line, and with its line GB5 brought into the plane
of C and BB. This being done, the point B5 will generally not
find itself in the line BB ; but we can shift A A towards or from
(7, moving consequently the plane GBB and the line BB in that
plane till the line BB gets B5 entered into it.

Thus all is completely clamped ; and the two straight lines of
motion of the points A and B relative to the desired frame in
which G is at rest, are found relative to each one of the configura-
tions ABC at the successive instants of the measurements. But

1884] REDUCTION OF MOTION TO SIMPLEST REFERENCE FRAME 393

those past configurations of the points A, B, and G, are already
lost to us ; and so we must proceed to find the lines A A and BB
relative to one or more future configurations of those three points
which are the only things that are to be available to us to make
measurements from. It is here to be distinctly noticed that the
lines of motions AA and BB, being fixtures in the desired frame,
may perfectly well be accepted as constituting that frame; or even
one of them along with the point C (which is also a fixture in the
desired frame) might equally well be accepted as constituting the
desired frame.

Now we have to observe that, from the nature of the data, and
of the operations performed in the kinematical model or mechanism,
and result arrived at in it, it must be the case that the lengths
A^AI, A2A3, A3A4 &c., and B^B^, B2B3) B3B4, &c., found in the
model as representatives of simultaneous travels of the real points
A and B relative to the desired frame, must be mutually pro-
portional. Hence, by continuing forward for the future a like
proportional division along BB for any arbitrarily marked
graduation along A A, we can by measurements from the model
foretell future instantaneous configurations of the points A, B,
and (7, and the situations of the fixed lines of motion A A and BB
relative to those future configurations. So at any future instant
when one of those prophesied configurations arrives, we shall have
the means of specifying relative thereto the lines AA and BB;
and these, as already explained, are to be accepted as the desired
frame; that is, as being a frame accomplishing all the requisites
of the problem.

METHOD II.— Reverting now to the stage arrived at just before
our commencement of branching out into the two varied methods,
and maintaining the state of things there attained to, we may
proceed by a second alternative method as follows: — It is to be
recollected that, in the state of things attained to, we have three
templet points Alt A2, A3, all in one straight line A A ; and three
other templet points Blt B2, B3, all situated in another straight
line BB', and that, while keeping the line A A at a changeless
distance from the point C, and regarding the line A A and the
point C as being at rest, and consequently regarding the points
Alt A3, A3) as being also all at rest, we can keep moving the line
BB, in the one freedom it possesses, and so we can alter continu-
ously the distances B^ and BJ}*, and we may readily further see

394 DYNAMICS AND ELASTICITY [58

that we can alter continuously the ratio of either of these distances
to the other. So let us ordain the requirement that we are thus
to keep moving the line BB in the freedom it possesses till we
attain the condition that

AS A.A.-.BA'.-.A.A.-.BA.

For the purpose of accomplishing this requirement we may use
(ideally at least) a mechanism of parallel rulers or parallel pro-
jectors, &c., which will now be briefly described. For guidance in
geometrical principles towards formation of the conceptions
intended, imagine a straight line placed intersecting the line.s A A
and BB. Let us name this line as the transversal, or refer to it
as the line TT. Imagine the points Alt A2, As, to be projected
to the transversal by parallel projectors; and imagine the points
so found on the transversal to be further projected to the line BB.
Call the points so found on BB, the points bl} b2, b3) in correspon-
dence with A1} A2, As, from which they have been respectively
derived. Now obviously we have by geometry,

Further it may easily be seen that we can gradually change the
directions (or clinures) of the two sets of parallel projectors until
we get the point 6j to coincide with Bl, and maintaining that
coincidence we can go on changing the directions of both sets of
parallel projectors till we get also 62 to coincide with B2. This
being done we can, by observing whether or not bs coincides with
B ascertain whether or not it be the case that

The general principle thus indicated can be applied to the case
immediately before us in a simplified combination by choosing to
make the transversal pass through the points A3 and Bl as in
fig. 2, where TT represents the transversal. The figure is to be
understood as being a pictorial representation on the paper, of
lines and points not themselves situated in the plane of the paper,
and not all existing in any one plane. Then take a pair of
straight lines kept parallel by mechanism (as for instance is the
case in some commonly used kinds of parallel rulers) and place
one of these lines so as to pass through Al and Bl and make the
other pass through Az. This second line being parallel to A A
(see fig. 2) must be in a plane with it and with the line A A and

1884] REDUCTION OF MOTION TO SIMPLEST REFERENCE FRAME 395

consequently with the transversal. So it meets the transversal.
These two parallel lines are represented in the figure as A1B1 and
A 2t2. So now we have, in the figure,

Take two other straight lines kept parallel by mechanism, and
place one of them across from t3 to B% and make the other pass
through A3, and then it will necessarily meet the line BB. So
these two parallel lines will be represented in the figure as t2B.2
and A3b3; and we shall have

Fig. 2.

Now in general it will result that 63 so found will not coincide
with Bs ; but let us now keep the line BB moving in the freedom
it possesses, and keep the two pairs of parallel lines maintaining
the conditions to which they have been set, and continue the
motion until the points 63 and B3 come to coincide, and bind these
two points to remain together ; or, in other words, bind the line
^363, when brought to pass through the point B3 hitherto
movable along the line BB, to continue holding the templet point
B3. Thus all will be clamped as long as the temporarily imposed
condition of changeless distance from the templet point G to A A
is maintained.

396 DYNAMICS AND ELASTICITY [58

But if now we change that distance, and fix on a new changeless
distance instead, while maintaining all the conditions already
attained to, the whole system will take up a new configuration
and will become clamped therein.

Or we might express this by saying : — Fix A A at an altered
distance from (7, and by going through the same process as before
we get one fixed configuration for the whole system. So if we
relax the condition of changeless distance of A A from C, the
whole system has one and only one freedom.

For the next step we do not require another complete templet.
We may use merely the lengths CA4 and CB4 got by measurement.
That is let us have a portable triangle with two sides CA4 and
CB4 given, but the angle between them left unknown, and that,
for our present operations, is the same as to say : — left variable.
Put the vertex C, or joint (7, of that portable triangle at the point
C of our model. Bring CA 4 into the plane CAA, and swing it
round till A4 comes into the line A A. Also put the rod or bar
CJB4 into the plane CBB ; and swing it round till B4 comes into
the line BB. This being done, the proportionality wanted,

that A^2 : B,B2 : : A,A4 : B,B,

will generally not have been instituted. But now, while main-
taining all the conditions already attained to, move A A varying
its distance from C, till that proportionality takes place as
indicated by the mechanism of parallel rulers, &c., already used,
but with some obviously necessary additions sufficiently suggested
by the explanations already given. Now the whole system
becomes clamped, and the problem is solved, or the rest is easy as
in Method I, the two straight lines A A and BB, being lines fixed
in the sought-for frame, and it being possible to find them for any
prophesied future configuration of the set of three points A, B,
and C, as has been explained at the close of the explanations for
Method I.

It becomes now convenient and desirable to examine into
some questions as to how many distinct elements of data from
measurement, or how many ascertained conditions from measure-
ment, are required for the solution of the problem ; and as to
whether there are more essentially distinct solutions than one in
various cases of the number of points used and the number of
conditions from measurement ascertained.

1884] REDUCTION OF MOTION TO SIMPLEST REFERENCE FRAME 397

It is to be recollected, as was pointed out near the end of the
explanation of Method I that the lengths A^A^ A2AS, A3A4, &c.,
and BiB.2, B.2B3, B3B4, &c., found in the model as representatives
of simultaneous travels of the real points A and B relative to the
desired frame, must be mutually proportional. But the conditions
of this mutual proportionality have been left unused in the
solution, and so we may see that in Method I we have used
redundant data. It is to be understood that the introduction of
any one complete templet brings in just two not three new
conditions. Though for it there are three sides measured, yet the
only conditions thereby ascertained are that when some one side has
a certain stated length, a second side has another ascertained length,
which is one condition, and that also at the same instant the third
side has another ascertained length which is another condition;
and this makes with the previous one only two in all.

In Method I after the stage up to which the procedure is
common to both Methods I and II ; we have — (a) templet 4
introduced involving two additional conditions from measurement,
and (6) templet 5 introduced, involving two additional conditions
from measurement. So in respect to these two templets 4 and 5
we have four conditions introduced.

And in the whole of Method I there are the following known
conditions unused : —

That ffi#2 = #

A 1^2 A.i

that ^1^2 _ B
AI<A.<I •A-i^

and that l=

That is, in all, three known conditions unused. So instead of
ascertaining 4 conditions by measurement and neglecting 3, we
might get the result by 4—3, that is one new condition from
measurement. Now in Method II we do demand from measure-
ment just one new condition, and we have no redundant informa-
tion. The one new condition so introduced is the condition
brought into use by the incomplete templet 4; videlicet, that when
GA has a certain stated length CB has another certain ascertained
length.

So, on the whole, in Method I we have from measurement
5 templets supplying two conditions each, that is, we have 10

398 DYNAMICS AND ELASTICITY [58

conditions from measurement; and, as shown already, we are
thus supplied with 3 redundant conditions ; and so 10 — 3 or 7
conditions from measurement, or independent data, must somehow
be enough.

Passing to Method II we see that in it we have 3 complete
templets supplying 6 conditions, and 1 incomplete templet
supplying 1 condition ; and we have got no redundant conditions ;
but we have just 7 conditions found necessary and brought into
use.

So the two methods agree in showing that the number of
independent conditions from measurement necessary to be supplied
is seven.

There is yet a curious matter which I have to adduce for
consideration. Many matters of interest may indeed remain for
further consideration or for mathematical investigation in connec-
tion with this subject ; but I do not at all profess to exhaust the
subject, and I shall only be glad if it be found that I escape from
offering inadvertently any importantly erroneous views.

What I do propose now further to put forward is some
scrutinies as to whether the problem entered on, in some of its
varieties, admits of duplicate or multiple results for accomplishing
its conditions; and to open out some views in relation to this
matter which appear to be true and to be of interest.

It is to be noticed that when we begin putting together our
templets for the kinematical model or mechanism for three
original moving points A, B, and (7, we have no means available
for knowing on which side of templet 1 we are to place the point
A2 of our templet 2, and on which side of the same we are to
place the point B2 of our templet 2. Further, it is to be noticed
that, under the restriction of our measurements being confined to
three of the original points only, we have no means whatever for
making the extra measurements, or taking the extra observations
that would supply us with means for choosing one side rather
than the other of templet 1, as that on which we ought to place
either Az or B2. To help our conceptions let us imagine among
the original moving points a reference frame relative to which the
original point C shall be at rest and which shall have no rotation
relative to the original secret frame ; and let us name this as the
vice-original frame and designate it briefly by the letter <£. Let
us imagine the original triangular plane AGE as having one of its

1884] REDUCTION OF MOTION TO SIMPLEST REFERENCE FRAME 399

two faces red and the other blue ; and imagine its face which at
the point A is anterior in its motion relative to the vice-original
frame to be red, and the one which at that point is posterior to be
blue. In respect to this it is to be noticed that the red face thus
specified though anterior at A may happen to be the posterior one
at B : but this need not give us trouble, and for brevity we may
speak of the red face which at A is anterior as being the anterior
face. Let the faces of all the templet triangles be coloured red
and blue correspondingly.

By going forward with considerations readily suggested by
what has just been set forth, we may obviously find that the
process of solving the stated problem for the case of only three
original points by the kinematical mechanism can bring out two
straight lines A A and BB really at rest relatively to the vice-
original frame, and consequently having all their points either at
rest or moving rectilinearly and mutuo-proportionally in relation
to the original secret frame : and further that the same process of
solving the stated problem can bring out another real true solution
in finding two straight lines which we may call A' A' and B'B'
which will be the images of A A and B.B in a plane mirror whose
plane always passes through the three points A, B, and C. The
two straight lines A' A', B'B' so found may be taken as lines fixed
in a frame which we may designate as <!>', and which will rotate
relatively to the vice-original frame <£, as also relatively to the
original secret frame. Now, as the motion of the original points
goes on making their distances apart increase unlimitedly, this
relative rotation between the frames <£' and <3> will be becoming
evanescent, and the two frames will be approaching unlimitedly
towards relative rest. So the solution which brings out the
frame <£>' approaches ultimately to identification with that which
brings out the frame 4> which is in agreement with the original
secret frame.

If now instead of using the three points C, A , and B, we use a
different group of three points C, A, and D, these will bring out
for us as solutions two frames 4> and <£>", of which the one <£> will
be identical with the frame <E> already found by the three points
C, A, and B. It follows from this (and it seems very obvious
that it could be brought out in various other ways), that for four
original points no frame in general could be brought out as a
solution except one in agreement with the original secret frame ;

400 DYNAMICS AND ELASTICITY [58

that is to say, a frame either at rest relatively to that original
frame, or having all its points moving rectilinearly and mutuo-
proportionally relatively to that original frame. One reason which
seems very decisive in favour of this conclusion is : — that if any
three of all the original points be retaining their distances apart
unchanging, then these three will themselves constitute a frame
<S> which will be in agreement with the original secret frame : and
then for any other one or more of the original points taken along
with these three, no frame will be possible to serve as a solution
except such as shall be in agreement with that one.

^
POSTSCRIPT.

The ideas noted in what follows had not completely occurred
to me till after the evening of the meeting of the Society when
the paper was read, and a suggestion towards their development
came from Professor Tait's paper of the same evening "On
Reference Frames." Thus it seems suitable to annex them here
as a postscript.

It may be noticed that in the case referred to in the last
sentence of the paper just before this postscript — the case of three
original moving points retaining their distances apart unchanging
— the method of procedure employed throughout the paper would
collapse because the points A and B would be at rest relatively to
the vice-original frame, and so the straight lines of motion A A
and BB previously used would become only two points. Yet a
solution is in this case even more readily available than in the
previously considered cases. It thus becomes desirable to find
some way of harmonising the two modes of thought or of procedure
so as to bring them into connection ; rather than to be content to
suppose that, in passing from one to the other, we should have
quite to . abandon the one mode of thought, and take up another
and quite unallied mode instead.

A satisfactory connection between the two presents itself, if,
instead of taking from the kinematic model only the lines of
motion A A and BB, as the basis for our desired frame, we take
from that model also the points Al and Bl on those lines, getting
them known by measurement of their distances from any future
points An and Bn, so that when, among the three original points
A, B, and C, the particular configuration AnCBn found in antici-

1884 J REDUCTION OF MOTION TO SIMPLEST REFERENCE FRAME 401

pation from the model shall come to exist, the old triangular
frame A$Bl shall become known to us relatively to the then
existing frame AnCBn. In this way of procedure, the solution, for
the case of A and B being, as well as C, at rest in the vice-original
frame, will come out simply by the distances AnA^ and BnBl being
each zero in length, and by the concomitant of this, that the old
frame A1CBl is to be found as being coincident with the new
momentarily existing and known frame AnCBn.

NOTE ON REFERENCE FRAMES. By Professor TAIT.

As I understand Prof. J. Thomson's problem [cf. ante, p. 386]
it is equivalent to the following : —

A set of points move, Galilei-wise, with reference to a system
of co-ordinate axes ; which may, itself, have any motion whatever.
From observations of the relative positions of the points, merely,
to find such co-ordinate axes.

It is obvious that there is an infinitely infinite number of
possible solutions ; because, if one origin moves Galilei-wise with
respect to another, and the axes drawn from the two origins have
no relative rotation, any point moving Galilei- wise with respect to
either set of axes will necessarily move Galilei-wise with respect
to the other. Hence any one solution suffices, for all the others
can be deduced from it by the above consideration.

Referred to any one set of axes which satisfy the conditions,
the positions of the points are, at time t, given by the vectors

«! + /3J for A , «2 + fat for B, &c., &c.

But it is clear, from what is stated above, that we may look on the
pair of vectors for any one of the points, say ax and & for A, as
being absolutely arbitrary: — though, of course, constant. We will,
therefore, make each of them vanish. This amounts to taking A
as the origin of the co-ordinate system. The other expressions,
above, will then represent the relative positions of B, G, &c., with
regard to A.

The observer on A is supposed to be able to measure, at any
moment, the lengths AB, AC, AD, &c. ; the angles BAG, BAD,
GAD, &c. ; and also to be able to recognise whether a triangle,
such as BOD, is gone round positively or negatively when its
corners are passed through in the order named. What this leaves
undetermined, at any particular instant, is merely the absolute

T. 26

402 DYNAMICS AND ELASTICITY [58

direction of any one line (as AB), and the aspect of any one plane
(as ABO) passing through that line. These being assumed at
random, the simultaneous positions of all the points can be
constructed from the permissible observations. But it is interest-
ing to inquire how many observations are necessary ; and how the
/3s depend on the as.

Thus, at time t, whatever be the mode of measurement of time,
we have equations such as follows : —

- a = «22 + 2Saafo . t + /322t2,
-b = Sw3 + S (CL& + j32a3) . t

For any one value of t we have n equations of each of the 1st and
3rd of these types, and n (n — 1)/2 of the 2nd, n + 1 being the
whole number of points. In all, n (n + l)/2 equations.

The scalar unknowns involved in these equations are (1) the
values of t; (2) «22, «32, &c. ; (3) &2, &2, &c. ; (4) Sa2«3, &c. ; (5)
S#A, &c.; (6) SaA, Sa.&, &c. ; and (7) 8 (*2& + &«,), &c.
Their numbers are, for (2), (3), (6), n each; for (4), (5), (7),
n (n — l)/2 each ; in all 3n (n + l)/2. Suppose that observations
are made on m successive occasions. Since our origin, and our
unit, of time are alike arbitrary, we may put t = 0 for the first
observation, and merge the value of t at the second observation in
the tensors of /32, /33, &c. This amounts to taking the interval
between the first two sets of observations as unit of time. Thus
the unknowns of the form (1) are m — 2 in number. There are
therefore

mn (n + l)/2 equations and 3n (n + l)/2 4- m — 2 unknowns.

Thus m = 3 gives an insufficient amount of information, but m = 4
gives a superfluity.

In particular, if there be three points only, which is in general
sufficient, 3 complete observations give

9 equations with 10 unknowns ;
while 4 complete observations give

12 equations with 11 unknowns.

Thus we need take only two of the three possible measurements,
at the fourth instant of observation.

1884] REDUCTION OF MOTION TO SIMPLEST REFERENCE FRAME 403

The solution of the equations, supposed to be effected, gives us
among other things, «22, «32, and Sa2as. Any direction may be
assumed for «2, and any plane as that of or2 and «3. From these
assumptions, and the three numerical quantities just named, the
co-ordinate system required can be at once deduced.

This solution fails if (#«2a3)2 = a./a32, or TV&& = 0 ; for then
the three points A, B, C, are in one line at starting. But this,
and similar cases of failure (when they are really cases of failure)
are due to an improper selection of three of the points. We need
not further discuss them.

But it is interesting to consider how the vectors /3 can be
found when one position of the reference frame has been obtained.
Keeping, for simplicity, to the system of three points, we have by
the solution of the equations above the following data : —

Sa,(32 = e, Sct3& = J, 8 («2& + &*3) =/, % = g, T& = g', S{3A = h\

where e, e ,f, g, g', h are known numbers; which, as the equations
from which they were derived were not linear, have in general
more than one system of values. The second, third, and sixth of
these equations give

Provided /3.2 is not coplanar with «2, «3, this equation gives, by the
help of the fifth above, a surface of the 4th order of which /92 is a
vector. But /32 is also a vector of the plane $a2/32 = e, and of the
sphere Tfi.2 = g. Hence it is determined by the intersections of
those three surfaces.

But if $ . «2aA vanishes, the equation above gives (by operating
with S . F«2a3)

0 = h(Vwtf- (/-£&«,) S.&V. «3Ta2a3 -f e'S. /92F.«2Fa2a3,
which gives a surface of the second order (a hyperbolic cylinder)
in place of the surface of the fourth order above mentioned. This
may, however, be dispensed with : — for /32 is in this case deter-
mined by the planes Sn^fy — e and S. a.2a3/32 = 0, together with the
sphere Tfi2 = g.

26—2

404 DYNAMICS AND ELASTICITY [59

59. SAFETY UNDER REPEATED AND VARYING STRESSES.

[The British Association appointed a Committee consisting
of Mr W. H. Barlow, Sir F. J. Bramwell, Prof. James Thomson,
Sir D. Galton, Mr B. Baker, Prof. W. C. Unwin, Prof. A. B. W.
Kennedy, Mr C. Barlow, Prof. H. S. Hele Shaw, Prof. W. C.
Roberts- Austen, and Mr A. T. Atchison for the purpose of obtain-
ing information with reference to the Endurance of Metals under
repeated and varying stresses, and the proper working stresses on
Railway Bridges and other structures subject to varying loads.

They reported in 1887 (see Brit. Assoc. Mancheste^, 1887,
report, page 424). It is understood the two passages here printed
from the report were drafted by Professor Thomson and sent to
Mr Barlow with the following letter.]

CRAIGPEATON, COVE,
DUMBARTONSHIRE,
23 Aug. 1887.

MY DEAR MR BARLOW,

I enclose two paragraphs such as you proposed that
I should send to you : — one relating to my views put forward in
my paper of Nov. 1848, and the other relating to my brother's
discoveries of May, 1865 as to Viscosity in Elasticity and recovery
by rest from some effects of fatigue. I may mention that my own
view of 1848, following on Hodgkinson's experimental results,
was amply verified by various easily made experiments which
I made soon after the paper was published. These were never
actually published in any printed paper by me but they were
made publicly known often in lectures and otherwise by myself:
and any person interested could easily test the matter by experi-
ments for himself.

I may also mention that I would despair of finding how to
give any brief recommendation for good new amended regulations
to be suggested to the Board of Trade.

The subject of the regulations if they are to be made much
better than at present would I think become very complicated.
You know of my advocacy of a change of practice by use of more
of the method of Force Tests.

Excuse my writing now briefly, being in great haste for post.

Yours truly,

JAMES THOMSON.

1887] SAFETY UNDER REPEATED AND VARYING STRESSES 405

[From the Report of the British Association, 1887, p. 424.]

In a report to the British Association in 1837, on strength
and other properties of cast iron, Mr Eaton Hodgkinson (Brit.
Assoc. Report for 1837, Part I. pages 362 and 363) made an-
nouncements, from his experimental researches, to the following
effect : — That in various experiments on transverse loading of bars
he had found visible permanent sets produced by such small
loadings as 1/30, 1/52, and 1/80 of the breaking weight ; showing,
he said, ' that there is no weight, however small, that will not injure
the elasticity'; and as a conclusion that 'the maxim of loading
bodies within the elastic limit has no foundation in nature'

Again, in the Brit. Assoc. Report for 1843, Part u. page 24,
Mr Hodgkinson, after detailing further experiments on the same
subjects, says: — "It appears from the experiments that the sets
produced in bodies are as the squares of the weights applied, and
that there is no weight, however small, that will not produce
a set and permanent change in a body, and that bodies when bent
have the arrangement of their particles altered to the centre ; and
when bodies, as the axles of railway carriages, are alternately bent,
first one way and then the opposite, at every revolution, we may
expect that a total change in the arrangement of their particles
will ensue."

Such assertions as those in MrHodgkinson's two communications
here referred to, if accepted in full, must necessarily induce very
uncomfortable feelings as to endurance of engineering structures.
Mr (now Professor) James Thomson, however, in a paper published
in the Cambridge and Dublin Mathematical Journal, vol. ill.
p. 252, Nov. 1848*, without abandoning the idea of there being
some real foundation in nature for prevalent opinions as to limits
of elasticity, showed how the elastic range of change of form
might, in many of the ordinary cases of materials newly prepared
by manufacturing processes, be found to be very narrow on account
of the existence of mutual strains or stresses among the particles
composing them — that thus permanent sets might be met with on
the application of very small loadings — that in this way, through
the ductile yielding of the more severely stressed parts, the range
of elastic action, or range of action within elastic limits, would be
greatly widened, and that after the application of a heavy load,
* [See supra, p. 334.]

406 DYNAMICS AND ELASTICITY [59

which the material could properly bear, subsequent applications of
any smaller loads would produce no new permanent set or alteration
— none, at any rate, in any way corresponding to those great and
alarming alterations indicated in Mr Hodgkinson's announcements.
(That paper of Professor Thomson's came, besides, under the
notice of practical men through its having been republished in
one or more of the engineering journals of the time; and it has
recently been republished in the article on " Elasticity " by Sir

William Thomson in the Encyclopaedia Britannica.)

*****

In a paper by Sir William Thomson, entitled " On the Elasticity
and Viscosity of Metals," published in the Proceedings of the Royal
Society for May 18, 1865*, an account is given of experimental
researches instituted by him and conducted in his laboratory in
the University of Glasgow, through which some new and previously
unsuspected properties in the elasticity of metals were discovered.
These cannot be fully described here in detail, but it may be
mentioned that the new results, of greatest interest and probably
of greatest practical importance, related to temporary and gradually
subsiding effects left in wires by previous elastic oscillations.
Energy was expended (dissipated) much more in any one torsional
oscillation of a wire which had for some time previously been kept
actively oscillating, than in a like oscillation either of the same or
of a different but similar wire after having been for some time
previously in a state of rest or of less active oscillation.

In the continuation of these experimental researches (after the
publication of the paper, it would seem) the effects of the kind of
fatigue and rest here referred to manifested themselves very
remarkably in the oscillation of wires kept almost constantly
in activity, during most days of the week, but getting rest usually
from Friday evening till Monday morning. The successive
oscillations diminished in their amplitude, by internal resistance
or some condition like viscosity in their elasticity, much less on
the Monday mornings, after their Sunday rest, than at other times,
succeeding closely to previous activity.

* [See Sir Wm. Thomson, Math, and Phys. Papers, Vol. in. pp. 22—26,
§§ 30—34.]

GEOLOGICAL

60. ON THE PARALLEL ROADS OF LOCHABER.

[Read before the Royal Society of Edinburgh, 6th March, 1848. Reprinted
from the Edinburgh New Philosophical Journal for July, 1848, Vol. XLV.
p. 49. On reading this paper, consult the Map of the Shelves or Parallel
Roads of Lochaber, in Vol. XLIV. of this Journal. — Reproduced on next
page.]

THE Parallel Roads, Shelves, or Terraces, of Lochaber, constitute
a wonderful inscription, traced by the hand of Nature, over the
surface of a wide range of mountains and glens. To interpret this
writing, and to disclose the story which these mysterious but clearly-
marked characters transmit, has long been an object of much
interest, as well as of great perplexity, to geologists. As yet,
however, no one has succeeded in arriving at an explanation of
the subject, which, after having undergone the scrutiny of others,
has given general satisfaction; and scientific men are still, perhaps,
as much divided in opinion as ever in regard to the nature of the
operations by which they suppose these terraces to have been
produced. Two papers, taking different sides on this question,
have appeared in the last two numbers of Jameson's Philosophical
Journal, — the first by Mr David Milne, and the second by
Sir George S. Mackenzie. The new and very interesting dis-
coveries which have lately been made by Mr Milne in his
researches among the hills, are brought forward by both writers in
confirmation of their respective theories. These discoveries, how-
ever, when taken in connection with the highly important principles
of the motion of glaciers recently developed by Professor Forbes,
appear to me to be far more strongly confirmatory of the leading
features of the explanation given by Agassiz ; at the same time
that they enable me to develop this explanation more fully,
modifying and correcting it in some degree, so as to make it

408

GEOLOGICAL

[60

ill

fSl ij i = j

1848] ON THE PARALLEL ROADS OF LOCHABER 409

accord with the new facts and principles, and thus putting it in a
form in which, to me at least, it appears so satisfactory as to leave
scarcely the slightest doubt of the agency of ice in the formation
of the Parallel Roads.

Mr Milne's paper may be regarded as consisting primarily of
two parts, — the object of the one being to prove that the terraces
are the beaches of lakes which have been maintained among the
hills by barriers occupying the lower parts of the glens ; and the
object of the other, to shew that these barriers consisted of earthy
detritus, and to explain the way in which he thinks they may
have been formed, and subsequently removed.

His explanation differs from those given by Dr MacCulloch
and Sir Thomas Dick Lauder in 1817 and 1818, principally in his
attributing the removal of the barriers not to any violent con-
vulsions of nature, but to the gradual operation of existing causes.
These, if I fully understand his statements, he supposes to be the
erosive action of the waters of the lakes themselves, combined with
that of rivers and streams. On this subject he says — " My ex-
planation of the Lochaber shelves depends entirely on the
supposition that the valleys were, in tiie lower parts of them,
filled up with detrital matter capable of being gradually worn
down and washed away." Sir George S. Mackenzie, although
there is much of his reasoning which I do not consider satisfactory,
appears to succeed completely in confuting the explanation given
by Mr Milne, so far as it depends on the supposed existence of
earthy barriers. On the other hand, Mr Milne proves, I think
beyond the possibility of doubt, that the Parallel Roads are the
beaches of ancient lakes, which have been maintained among the
mountains by barriers across the lower parts of the glens.

With reference to objections to the supposed existence of
barriers which had previously been brought forward, Mr Milne
remarks — " These objections resolve entirely into the difficulty of
explaining the disappearance of the barriers, which must have
dammed back the water in the valleys ; but it would be no good
reason for rejecting an explanation founded on the existence of
barriers, even though we could not very clearly account for the
disappearance of them, provided that there is direct and conclusive
evidence that such barriers existed. Now, I conceive that there
is such evidence furnished by the considerations before referred
to." Ideas similar to these of Mr Milne had also occurred to

410 GEOLOGICAL [60

Sir Thomas Dick Lauder nearly thirty years ago, and, in a paper
which he laid before the Royal Society of Edinburgh, they are
expressed in the following terms : — " I believe it will be readily
admitted, that it is much easier to suppose the existence of former
barriers, than to discover the means which operated in their
removal ; but it must be also granted, that the difficulty of
accounting for the destruction of such large masses, does not by
any means imply that they never had any being at all, particularly
where a number of facts remain to lead us to an opposite con-
clusion. From all the present appearances it is extremely probable
that the barrier of Loch Roy was not only very thin, but^of soft
materials, at the two parts which have been removed."

Thus, both Sir Thomas Dick Lauder and Mr Milne have come
decidedly, and, I think, with good reason, to the conclusion that
barriers did exist ; but then we are by no means obliged to
assume, that these were composed of earthy materials. It is
in this assumption, in fact, that all the difficulties connected with
the explanations given by these two writers are involved ; and to
me it seems perfectly clear that the barriers in reality were
formed of glaciers.

The glacial explanation of the Parallel Roads given by Agassiz
in his paper in Jameson's Journal for 1842, was necessarily im-
perfect in its details. Sufficient facts in regard to the phenomena
of the terraces themselves, and true principles of the motion of
glaciers, were then wanting. Had these been within the reach of
Agassiz, he could easily have modified his explanation so as to
remove all valid objections which have been brought forward
against it, and could have shewn the invalidity of others which
are still adduced, but which, I think, will not be admitted by
those who have duly appreciated the principles of the viscidity of
glaciers, as developed in the theory of Professor Forbes. The
object of Agassiz, however, at that time, was probably rather to
adduce the Parallel Roads as confirming his grand idea of the
former extensive prevalence of ice in these latitudes, than to enter
fully into the details of the mode in which the roads had been
produced; and in representing his supposed glaciers on the map
which accompanies his paper, his intention was, perhaps, not so
much to assert that the glaciers had acted exactly in the way he
indicated, as to illustrate the supposition that glaciers, acting in
some such way, would be found, in the end, fully to explain all

1848] ON THE PARALLEL ROADS OF LOCHABER 411

the phenomena. Be this as it may, Mr Milne succeeds in shewing
that the explanation by means of the supposed glaciers is incon-
sistent with observed facts. He then goes on to assert, that
glaciers could not possibly have penetrated to the places where
their presence would actually have been required. This state-
ment, of course, constitutes the turning point of the whole
argument, since, if it were correct, it would overthrow the glacial
explanation. I hope, however, to be able, in what follows, to give
good reasons against its soundness ; but, in the meantime, it will
be necessary to advert to the facts which invalidate, in its details,
the explanation given by Agassiz.

Previously to the researches of Mr Milne, it had been known
that there exist three "summit-levels" or " water -sheds" in con-
nection with three of the Parallel Shelves ; but the existence of
a fourth had not been noticed, and it had even been asserted by
Mr Darwin*, that "the middle shelf of Glen Roy is not on a

* [From Life and Letters of Charles Darwin, Autobiography, p. 68. " During
these two years I took several short excursions as a relaxation, and one longer one
to the Parallel Roads of Glen Roy, an account of which was published in the
Philosophical Transactions [1839, pp. 39—82]. This paper was a great failure,
and I am ashamed of it.

" Having been deeply impressed with what I had seen of the elevation of the land
in South America, I attributed the parallel lines to the action of the sea; but I had
to give up this view when Agassiz propounded his glacier-lake theory. Because no
other explanation was possible under our then state of knowledge, I argued in
favour of sea-action ; and my error has been a good lesson to me never to trust in
science to the principle of exclusion."

In the paper by L. Agassiz contributed to the Geological Society of London on
Nov. 4, 1840 (Proceedings, Vol. m. pp. 327 — 332), which was fundamental in the
identification of glaciation as a prime agent in geology, the following passage
occurs (p. 332) at the end of a general argument, which is the earliest statement
of a glacial theory of the Parallel Roads, and was derived from investigation on the
spot : —

"Another class of phenomena connected with glaciers is the forming of lakes
by the extension of glaciers from lateral valleys into a main valley : and M. Agassiz
is of opinion that the parallel roads of Glen Roy were formed by a lake which was
produced in consequence of a lateral glacier projecting across the glen near Bridge
Roy, and another across the valley of Glen Speane. Lakes thus formed naturally
give rise to stratified deposits and parallel roads or beds of detritus at different
levels."

For the literature of this subject see More Letters of C. Darwin, Vol. n. pp. 171
— 2, and Lyell's Antiquity of Man, 1863, pp. 252 — 64. For a modern account of
the working out of the details of the glacial theory, which may be compared with
the views given in the text, see Sir Archibald Geikie's book on the scenery of
Scotland in relation to its geology.

Sir J. D. Hooker, writing to Charles Darwin from the Himalayas in 1849,

412 GEOLOGICAL [60

level with any water-shed." Mr Milne has, however, found the
wanting water-shed in Glen Glaster, a small glen which, though
branching up from Glen Roy near the bottom of it, does not
appear to have been visited, and certainly has not been correctly
described by any former observer. But this is not all. Mr Milne
has also traced the channel of an ancient river, proceeding from
the water-shed in question, down into Glen Spean, and there
terminating in a huge delta, or alluvial deposit, at the only shelf
which winds round the sides of the latter glen, thus marking the
point where the turbid waters of the river were swallowed up
under the stagnant surface of the lake which, by these1* same
indications, is palpably shewn to have stood in Glen Spean on a
level with the lowest shelf, at the time when Glen Roy was
occupied with water to the height of the shelf next above.

In connection with these circumstances, Mr Milne finds that
the uppermost shelf of Glen Roy does not, as was erroneously
indicated on Sir Thomas Dick Lauder's map, run round
the sides of Glen Glaster, but that it suddenly stops short in
Glen Roy, just above the entrance to that smaller tributary
glen.

From this we conclude, that the barrier which blocked up
Glen Roy, so as to occasion the formation of its highest shelf, must
have disconnected it from Glen Glaster, and thus forced it to
discharge its surplus water into the valley of the Spey by the
summit-level at its head, instead of permitting it to discharge by
the lower summit-level at the head of Glen Glaster, and down by
the ancient river-channel into Glen Spean, — a course which must
have been followed by any water occupying Glen Glaster, or
communicating with it uninterruptedly.

Now, to explain the formation of the highest shelf of Glen Roy,
Agassiz supposed one glacier, in the lower part of Glen Spean, to
have extended across from Ben Nevis to Moel Dhu ; and another,
farther up that glen, to have issued from the valley of Loch Treig;

independently identified the parallel roads as the beaches of glacial lakes, on the
basis of his experience in that region (Life and Letters of C. Darwin, Vol. i.
p. 376). At this time Lyell, as well as Darwin, seems to have attributed them
to marine action. In 1861 Darwin, who had by that time abandoned the early
views advanced in his Phil. Trans, memoir of 1839, writes to Hooker (More Letters,
Vol. n. p. 190), " It is I believe true that Glen Boy shelves (I remember your
Indian letter) were formed by glacial lakes." See Sir W. Thiselton Dyer's obituary
notice of Sir J. D. Hooker, Proc. Eoy. Soc,, B, 1912.]

1848] ON THE PARALLEL ROADS OF LOCHABER 413

the two being sufficiently high and extensive to maintain the
water between them, and, of course, also the water in Glen Roy, at
the level of the shelf under consideration. In confirmation of this
supposition, he stated that the shelf is marked on the south side
of Glen Spean, between the sites of the two supposed glaciers.
Were the supposition true, the shelf should certainly be marked
in that situation, and also round Glen Glaster ; but, according to
Mr Milne, it is to be found in neither of these places. The middle
shelf of Glen Roy, according to Agassiz, should also occur in Glen
Spean, between the two supposed glaciers ; but Mr Milne asserts
that, in fact, it does not. Thus, then, the glaciers supposed by
Agassiz will not satisfy the conditions of the question; nor will
any other system of blockage do so, except one, according to which
Glen Glaster would, for a certain period, have been separated from
Glen Roy.

We are, therefore, if we proceed on the supposition of the
agency of glaciers, led to the conclusion, that the one which
stopped up the mouth of Glen Roy to form its highest shelf, must
have extended up that glen beyond the mouth of Glen Glaster.
It must also have blocked up Glen Collarig nearly to the place
named the Gap. Then, to explain the formation of the middle
shelf, it is only necessary to suppose that the glacier retired
a little, so as to connect Glen Glaster with Glen Roy. The water
in the latter would immediately begin to discharge itself by the
ancient river-course before mentioned, and its surface would thus
be lowered to the level of the middle shelf. Lastly, the lowermost
shelf of all would be formed when the glacier retired to near the
mouth of Glen Spean.

Mr Milne, however, asserts that, on account of the character of
the mouth of Glen Roy, in regard to levels, direction, and distance
from Ben Nevis, such a glacier as I have described could not have
existed ; but there does not appear to me to be any real difficulty
in the supposition.

The following considerations will, I think, tend to render this
clear. Of all climates capable of generating glaciers, there are
two extremes which must produce two corresponding extremes in
the mode of distribution of the ice on the surface of the earth.
The one of these extremes of climate may be instanced as occurring
in Switzerland, and the other in the Antarctic Continent recently
discovered by Sir James Clarke Ross. In Switzerland the mean

414 GEOLOGICAL [60

temperature of the comparatively low and flat land is so much
above the freezing point, that the ice no sooner descends from the
mountains than it melts away ; and it is thus usually prevented
from spreading to any considerable extent over the plains. In the
Antarctic Continent, on the contrary, the mean temperature is
nowhere so high as the freezing point. The ice, therefore, which
descends from the hills, unites itself with that which is deposited
from the atmosphere on the plains ; and the whole becomes con-
solidated into one continuous mass, of immense depth, which glides
gradually onward towards the ocean. The portions which are
protruded out to sea break off, and are floated away as icejbergs ;
the remainder being left, presenting to the sea a perpendicular
face which rises, in insurmountable cliffs, to the height of from
150 to 200 feet above the water, and extends below the water to
the depth of perhaps 1000 feet.

Now, a climate somewhere intermediate between these ex-
tremes appears to be that which would be requisite to form the
shelves in the glens of Lochaber. The climate of Switzerland
would be too warm to admit of a sufficient horizontal extension of
the glaciers ; that of the Antarctic Continent too cold to allow the
lakes to remain unfrozen. If the climate of Scotland were again
to become such that the mean temperature of Glen Spean would
be not much above the freezing point, there seems to be every
reason to believe that that glen would again be nearly filled with
an enormous mass of ice; while its upper parts, and also Glen
Roy, would be occupied by lakes, which would once more beat
upon the ancient and long-deserted beaches, — that the rivers
would resume their former channels, flowing out of the lakes by
the summit-levels between the glens,— and that the ancient aspect
of the country would, in all respects, be again restored.

It will perhaps be objected, that in imagining the ice to make
its way into Glen Roy, we are supposing it to flow up hill. A
semifluid mass, however, so long as its upper surface slopes down-
wards, cannot be regarded as flowing up hill, no matter what may
be the form of the bottom on which it rests. If a slightly-inclined
trough or channel have an opening made in one side, at the middle
of its length, and if a stream of thick mud be kept flowing into it
by this opening, the mud will not all turn suddenly round towards
the lower end of the channel, but a portion of it will flow in the
opposite direction, apparently up hill, till its surface comes to

1848] ON THE PARALLEL ROADS OF LOCHABER 415

meet the bottom of the channel at a level little, if at all, below
the surface of the mud at the side entrance.

In confirmation of the views just brought forward, regarding
the possible horizontal extension of the glaciers, I may refer to
the evidence given by Professor Forbes, in his Travels in the Alps
(page 50), of immense erratic blocks having been conveyed by
glaciers from the main chain of the Alps across all the inequalities
of the great plain of Switzerland, and deposited high on the hills
round the Lake of Neufchatel ; the total distance travelled over
being 60 or 70 miles, and the total declivity due to their descent
being certainly not more than 1° 8', and probably not half so
much.

Glen Gluoy, in regard to its blockage, seems to have been
quite independent of all the other glens to which I have as yet
alluded. A glacier occupying the present site of Loch Lochy, and
receiving supplies from the various neighbouring mountains, would
appear to afford a sufficient explanation of the phenomena observed
in this glen. Mr Milne has, however, discovered in it a shelf
which is lower than the one previously known, and which does
not appear to be in connection with any summit-level. If this be
the case, we may suppose that, while the lake was at the level of
this second shelf, its discharge took place by the present mouth
of the glen, through an elevated channel in the moraine of the
glacier. The lake would therefore have resembled almost exactly
the Lac de Combal and the Matmark See, described and figured
in the work by Professor Forbes to which I have already referred
(pp. 193 and 345).

There is, however, a circumstance connected with this shelf
which seems to me to involve some difficulty. As represented by
Mr Milne, its terminations, on both sides of the glen, are farther
from the mouth of the glen than those of the shelf abov\ In
fact, the upper shelf is shewn round the sides of Glen Fintec,
while the lower shelf is made to stop short without reaching the
entrance to that glen. Should this representation be really
correct, it would appear to involve the supposition, that the
glacier, when at the lower level, penetrated farther into Glen
Gluoy than it did when at the higher level. Now the question
arises, — Is it likely that this could have been the case ? Perhaps
light may be thrown on the subject by some curious circumstances
connected with the Lac de Combal. The glacier which occasions

416 GEOLOGICAL [60

the damming up of this lake has actually retired a considerable
way down the glen in which the lake is situated, since the
deposition of that part of its moraine which now retains the
water; and yet the surface of the glacier is some hundreds of feet
higher than that of the lake. Besides this, the glacier, at a point
farther from the head of the glen, threatens to overwhelm with its
moraine the channel of the river by which the superfluous water
of the lake is at present discharged. How imminent the prospect
of this occurrence really is, may be judged from the fact, that it is
necessary annually to remove the debris thrown down by the
glacier on the road which, together with the river, winds l^irough
the bottom of a deep ravine, enclosed on the one side by the
moraine of the glacier, and on the other by the continuation of
the hill which forms a side of the glen containing the lake.
Should the glacier force itself even a very little farther in this
direction, the surface of the lake would not only be raised above
its present level, but its horizontal extension towards the lower
part of the glen would be increased. The beach of the lake at
present existing, together with that of the new one thus formed,
would therefore exhibit exactly the peculiarities which, according
to the representation of Mr Milne, appear to exist in the two
shelves of Glen Gluoy. This fact is enough to make the difficulty
appear to be not insuperable. The simplest view, however, to
take of the subject may, perhaps, be to suppose that the glacier
which occasioned the formation of the higher of the Glen Gluoy
shelves, had at some period protruded a terminal moraine as far
up the glen as the terminations of the lower shelf; that on the
final retiring of the glacier this old moraine served as a barrier to
dam up the water to the level of the lower shelf, and that it has
been subsequently washed away by the river flowing over it.

I have thought it right to point out the foregoing difficulty for
the consideration of those who may have it in their power to gain
further information on the subject. Should any mutual action of
a glacier and its moraine have occasioned the peculiarity in
question, we might expect to find some remains of the moraine
between the terminations of the upper and those of the lower
shelf. It may here be remarked, that there is not the same
difficulty in accounting for the removal of this moraine, as for that
of the barriers supposed by Mr Milne to have existed at the
mouths of the other glens. For, in this instance, the water from

1848] ON THE PARALLEL ROADS OF LOCHABER 417

the lake of Glen Gluoy must have discharged itself over the top of
the moraine; while, in the case of the other glens, it certainly
flowed out by the summit-levels between the glens; and would,
therefore, have no power of cutting away the barriers.

There is, in the Lochaber district, still another glen, containing
a shelf, which was discovered by Mr Darwin, and described by him
in the Philosophical Transactions of the Royal Society of London
for 1839. This glen is situated near Kilfinnan, at the north-
eastern extremity of Loch Lochy. The shelf in it is stated by
Mr Darwin to be in every respect as characteristic as any shelf in
Glen Roy. He believes it to be perfectly horizontal ; and, in
connection with it, he discovered a water-shed, similar in its
nature to those which have been already mentioned. Now, as
this author remarks, in regard to any explanation by means of
earthy barriers, " the discovery of the shelf at Kilfinnan increases
every difficulty manifold." Every additional glen containing a
shelf, in fact, requires us to assume the deposition of an additional
barrier, and the subsequent removal of this by causes which have
left the shelves undisturbed. To admit, at the mouth of even a
single glen, of a barrier of such a peculiar nature as would enable
it to stand for a long time, but at last to be swept away, although
no river flowed over it, seems difficult enough ; but to imagine
that numerous glens should chance to be placed in such peculiar
circumstances, appears to be quite unnatural; no sufficient and
generally-acting cause being assigned for the repetition of the
supposed phenomenon. On the other hand, the existence of the
shelf in question is exactly what should have been expected,
according to the glacial theory I have maintained. The same
mass of ice occupying Loch Lochy, which I have supposed to have
been instrumental in forming the shelf in Glen Gluoy, would, to
all appearance necessarily, have blocked up also the glen at
Kilfinnan, and thus have produced the shelf which is really found
to exist round its sides, on a level with the water-shed at its top.
Mr Milne himself mentions the occurrence, in various parts of the
Highlands, of other glens containing shelves, none of which have,
however, been so carefully investigated as those we have been
considering. According to what I have already said, this would
appear to add to the difficulties of the explanation by means of
earthy barriers, and to confirm the one I have given, depending
on the agency of a climate such as would cover with a thick

T. 27

418 GEOLOGICAL [60

bed of ice almost the whole surface of the land in the neighbour-
hood of high mountains.

It will be unnecessary for me to enter at length into a discus-
sion of the diluvial theory of the parallel roads, given by Sir George
Mackenzie, as, after a full consideration of it, it does not seem to
me to be capable of explaining the observed facts. I may,
however, mention some of the leading objections which I would
bring against it. During the sinking of the supposed wave, on
the arrival of its surface at each successive summit-level, there
would be no sudden check to the flow of the water through the
glens, nor even to the rate of depression of the general surface of
the wave ; but even if some material alteration in the flow of the
water were to occur at those particular occasions, there seems to
be no reason to suppose that these vast shelves would be the
result. No attempt, besides, is made according to this theory, to
shew why the various shelves should be expected to stop short at
the particular places where, by observation, they are found to do so.

An objection which has been urged by Mr Lyell against the
glacial theory of the parallel roads must not be left unnoticed.
He thinks there are proofs to be met with in various parts of
Scotland of great changes having occurred in the relative levels of
the sea and land ; and he supposes that such changes would have
destroyed the horizontality which is found to characterise the
terraces. Now, there is probably no doubt that important changes
in the elevation of the land have occurred since the commencement
of the glacial period, but I do not think that any proof can be
given of their occurrence since its termination. In other words,
I think no proof can be adduced, that, ever since the last great
disturbance of the land, the climate has been so warm as to
preclude the supposition of the existence of glaciers round Ben
Nevis. Could this, however, be proved, still it does not appear to
me that it would invalidate the glacial theory of the terraces. It
is easy to conceive that the whole of Scotland might participate
in a general elevation or depression; each part remaining un-
altered in regard to inclination to the horizon ; and even were we
to suppose the south of Scotland to have risen 30 feet, while the
north remained stationary, and the intervening parts moved in
proportion to their distances from the north, the utmost deviation
from horizontality which would thus be produced in the terraces
would not exceed a foot of difference between the levels of the

1848] ON THE PARALLEL ROADS OF LOCHABER 419

northern and southern extremities of any one of them ; an amount
which would be quite imperceptible by any mode of measurement
which could be applied on surfaces so uneven.

In conclusion, I may remark, that, in calling in the aid of
glaciers towards the explanation of the Parallel Roads, no gratuitous
or unsupported assumption is made. So many various and inde-
pendent proofs of the existence of a glacial climate in these
countries, during some of the most recent geological periods, have
been accumulated, especially within the last few years, that we
may now regard it as an established fact, and use it like a
stepping-stone to assist us in farther investigations. In addition
to other proofs of a cold climate derived from organic remains, and
from effects which appear to have been produced by icebergs
floating at sea, indications of glaciers, in some instances of the most
unequivocal character, are to be met with in various mountainous
parts of Great Britain and Ireland. Such appearances, more or
less satisfactory, have been pointed out by various authors, of
whom it may be sufficient to mention Buckland, Lyell, Bowman,
Agassiz, Maclaren, and Forbes. In the island of Skye, in particular,
among the Cuchullin Hills, which have been lately explored by
the last- mentioned author, Professor Forbes, there are to be seen
more striking and indisputable traces of glaciers than in any other
locality which has, as yet, been examined. This is in a great
degree to be attributed to the durable nature of the hypersthene
rocks of which those hills are composed ; a property which has
caused their surfaces to retain not only the general forms, but
also the most minute markings produced by the glaciers; and
which, at the same time, has prevented these from being concealed
under a coating of decayed materials. The face of the country
seems, in fact, to have retained, almost absolutely unaltered, all
the appearances which it presented on the retiring of the ice.

In the Lochaber district, among other indications of the action
of glaciers, Agassiz has pointed out one which is interesting in
itself, and more so when taken in connection with the foregoing.
At the mouth of Loch Treig, the rock consists of gneiss, inter-
sected by veins of quartz. The quartz everywhere projects two or
three inches above the gneiss, its upper surface being polished and
striated, exactly as is the case with quartz veins exposed to the
action of glaciers at the present day. It is clear that the gneiss
and the quartz had originally been planed down to one even

27—2

420 GEOLOGICAL [61

surface; and that the gneiss, not being perfectly durable, has since
decayed away, and thus left the quartz veins standing in relief.

It would be out of place for me here to enter at greater length
into the question as to the former prevalence of glaciers, or of a
glacial climate. For farther details, I must refer to the authors
who have discussed the subject, particularly to those I have
already mentioned.

61. ON FEATURES IN GLACIAL MARKINGS NOTICED ON SANDSTONE
CONGLOMERATES AT SKELMORLIE AND ABERFOIL.

V

[From the Report of the British Association, Southampton, 1882, p. 537.]

WHEN glacial striation is met with on rock faces, it may often
be a matter of interest to find in which way along the direction of
parallelism of the striae the abrading or polishing ice must have
advanced. Casual observers, unskilled in the scrutiny of glacial
phenomena, may sometimes too hastily assume, when they find
the lines of the striae inclined to the horizon, that the ice has been
moving over the striated rock face or hill-side in the down-hill
direction of the striae. The direction of the motion of the ice
along the striae, however, cannot generally be safely inferred from
mere local configurations of the land; and, in some cases, the
configuration of the land, whether locally regarded or considered
in wide scope, may afford no decisive proof at all as to which way
the ice has advanced along the striae.

In the rather limited researches which the author has had
opportunity to make in respect to glacial phenomena in geology,
he has felt interest in seeking for indications presented by the
striated rock-faces themselves, which might conclusively shew in
which way the ice must have advanced. He wishes, in the present
paper, to make mention of one or two rather remarkable indications
of this kind which he has met with in the last two years.

At Skelmorlie, on the Firth of Clyde, at a height of about 150
or 200 feet above the sea, he has found glacially striated surfaces,
on red sandstone containing pebbles of quartz and of other kinds
of stone. Many of these pebbles projected considerably out from
the general smoothed and striated surface of the sandstone, and
from each of such pebbles there extended to one side a ridge
of the sandstone, like a tail ; — the sandstone being there worn
away less than at other places devoid of the protecting influence

1882] ANALYSIS OF GLACIAL MARKINGS 421

of any hard protuberant pebble. The manner in which the
protection had been given must have been this: — The ice, in
passing over the protuberant hard pebble, must, in virtue of its
plasticity, have had a groove moulded into it by the pebble, and
this groove passing forward from the pebble in the motion of the
ice, must have worn away the sandstone facing to it less than would
the other parts of the ice-face wear away the sandstone facing to
them. The length of the noticeable tail would depend mainly on
the distance that the ice could advance before the groove in it
would be gradually obliterated. A pebble of the size of a bean, for
instance, might often be found to have a tail visible for a length
of five or six inches, or perhaps from that to a foot; and larger
pebbles might be seen to have tails two or three feet in length.

Again, on the recent visit to the railway cuttings near Aberfoil,
referred to by the author in his previous communication*, a
remarkable example was found of a glacially worn and finely
striated conglomerate rock face. The situation of this is at
Ballanton, about a quarter of a mile from Aberfoil. The hard
pebbles were of various sizes, and many might be of sizes such as
those of beans, and eggs, and large potatoes. Some of them were
worn away by the ice continuously with the surrounding sandstone
matrix; but those of them which projected shewed very conspicuous
tails, many of which might be four or five feet long or more.

Various other indications, presented by the striated surfaces
themselves, of the direction along the striae in which the motion
of the ice has been made, may occasionally be found. Doubtless
none can be more strikingly remarkable than the tails extending
from hard pebbles or other hard nodules, or hard veins, included
in the ice-worn rock. The author wishes, however, to mention
that on making minute examination, by a magnifying lens, of the
scratches on worn quartz pebbles in the striated sandstone at
Skelmorlie, he was able to find also in these very small markings,
indications which appeared clearly to shew the direction of the
motion of the ice, and that these indications were perfectly in
agreement with those given by the tails extending from the
pebbles along the striated sandstone surface.

* [" Mention of an example of an Early Stage of Metamorphic Change in Old
Bed Sandstone Conglomorate, near Aberfoil," Brit. Assoc. 1882, p. 536. Not here
reprinted. It refers to distorted pebbles similar to those described in H. C. Sorby's
letter, p. 252, supra.]

422 GEOLOGICAL [62

62. ON THE JOINTED PRISMATIC STRUCTURE IN BASALTIC

KOCKS.

[Abstract. From the Transactions of the Geological Society of Glasgow,
8th March, 1877.]

THE views presented in the following paper have in great part
been previously brought forward and published on some other
occasions, but not hitherto in any such way as to become satisfac-
torily accessible among geologists. The fundamental ideas and
primary observations on which they were based were submitted by
the author to the Belfast Natural History and Philosophical Society
in a paper read on November 26, 1862, and the subject was shortly
afterwards brought under the notice of the British Association at
the Newcastle Meeting in 1863, and a brief but complete account
of the chief points is to be found printed in the Association's
Report for that year. A fuller account of the author's views,
with his discussion of the prevailing views of others, is printed
in the Annual Report of the Belfast Naturalists' Field Club for
1869-70, as an abstract of a paper read by him to that Society
in November, 1869. He was afterwards requested to bring the
subject before the Geological Society of Glasgow; and the present
paper contains a fuller exposition than any previous one, and
includes the discussion of a few facts which have later come under
notice.

Basaltic Rocks, and rocks generally of the trappean class
(which comprises most of those that have originated as volcanic
lavas), are very frequently to be found divided into prismatic
columns, more or less regular in form, and the columns are some-
times found to be divided into short lengths by cross fractures or
surfaces of easy partition, which show a remarkable regularity of
form. The columns, however, it is to be particularly noticed, are
quite devoid of the kind of exact regularity that belongs to
crystals. They vary in the number of their sides from three to
eight or nine, and it seems that occasionally a column may be
found with so many as twelve sides. The angles between the
sides have no regularity whatever ; those seen in the end or cross-

1877] ON JOINTED PRISMATIC STRUCTURE IN BASALTIC ROCKS 423

joint or cross-parting of a column, being generally unequal among
one another, and the magnitude or obtuseness of any one angle being
subject often to considerable variation along the length of the
column. Also, in passing along the length of a column, a face
may often be found becoming narrower and narrower till at last
it dies out, and the adjacent faces may be noticed to twist round,
altering their angle of mutual inclination in passing along the
column. For such reasons as these, a notion which has often
been vaguely entertained, that the columns may be of the nature
of gigantic crystals, is to be set aside at once as untenable.

The columns are often remarkably straight and parallel — some-
times they radiate, or, we may rather say, converge, like the
spokes of a wheel ; and sometimes, though more rarely, they are
curved. They are to be met with in various sizes. Sometimes
they may be found only an inch across, and sometimes so much as
9 feet ; and when small in diameter they may often be short in
length — perhaps a few inches or a foot or two long; while columns
of larger sizes are often found extending to lengths of 50 or 100
feet, and sometimes even to 200 or 300 feet. In a horizontal
layer of basalt, or trap rock, the columns are vertical ; in a dyke
they are perpendicular to the rock faces which have confined the
basalt, trap, or lava in its molten state ; and, when occurring in a
trough or valley of rock, with irregular configuration of its sides
and bottom, some of them may occasionally be found curved along
their length. As a general rule the columns are found to abut
perpendicularly against the rock faces which have confined their
substance in its molten state. The descriptive particulars just
given are collected from many observations and sources of infor-
mation, and seem to be fairly trustworthy so far as they go. But,
in the absence of far more trustworthy knowledge of the physical
conditions under which the structure has originated than has as
yet been attained to, it must be supposed that there may be yet
other important features remaining which have hitherto escaped
notice, or have been imperfectly described. The well-known and
generally-admitted features referred to in the description just
given seem to indicate very clearly that the direction of the
columns has been somehow imparted to them by the cooling sur-
faces into contact with which the molten substance has been
poured. It seems not unreasonable to suppose that the
columns have commenced from the colder surface, proceeding

424 GEOLOGICAL [62

thence into the cooling mass with a tendency to perpendicularity
to the colder surface, and that in advancing farther forward longi-
tudinally, they have had a tendency to proceed perpendicularly
to successive isothermal interfaces in the cooling mass; or, at
least, that their longitudinal configurations, whether straight or
curved, and whether parallel or radiating, may have been decided
in an important degree by influence of the configurations of the
isothermal interfaces existing in the cooling mass during their
growth as columns.

Of the opinions which have commonly been entertained among
geologists as to the manner in which the jointed prismatic structure
has originated, none have appeared to the author satisfactory.
They have very generally involved one or other, or a combination
of both of the two following principles : —

1st — Prismatic fracture by shrinkage in cooling, like the crack-
ing which may be observed in starch or mud in drying.

2nd — An assumed spheroidal concretionary action of the lava
or basalt in solidifying from the molten state.

He gave sketches in fuller detail of the views put forward by
several of the leading geologists in various parts of the world, as
expressed by those writers themselves, who have either proposed
them or have at least promulgated them with favour, though in
some cases with vagueness — the natural result, he said, of attempt-
ing to explain intrinsically untenable views. Sir Charles Lyell,
writing, for instance, in his Elements of Geology, under bhe heading
" Columnar and Globular Structure," while appearing to put forward
with favour the spheroidal concretionary theory, seems also to be
affected with this character of vagueness. Dr Daubeny, Beete
Jukes, and several others, with much more boldness maintain the
spheroidal concretionary theory under various modifications of its
details. Dr Daubeny*, for instance, believes that the cause for
the columnar arrangement of trap is to be found in the spheroidal
or globular structure often shown in these rocks during their dis-
integration by exposure to the weather. He then says, " It is
evident that a series of globular concretions of trap placed in close
contact whilst in a pasty condition, or in a state of transition from
fusion to solidity, would be by mutual pressure converted into a
succession of jointed columns, which, owing to slight differences

* Daubeny, Volcanos, 2nd edition, 1848, pp. 660 and 661.

1877] ON JOINTED PRISMATIC STRUCTURE IN BASALTIC ROCKS 425

in the compactness and consequent softness of the several parts of
the mass, would rarely be exact in their sizes and in the number
of their sides, but would exhibit all those variations which in
that respect columnar basalt commonly displays." Dr Daubeny,
in connection with these views, describes a " natural grotto,"
called the Kase Keller, at Bertrich, near the Mosel, between
Coblenz and Treves [see Fig. 1, p. 426]*. It is called the
Kase Keller (Cheese Cellar) from the resemblance to Dutch
cheeses piled up in columns which is presented by the roughly
spheroidal joints of which its columns are made up. He says
" It beautifully illustrates the origin of the jointed columnar
structure which this rock so often assumes, since a little more
compression would have reduced these globular concretions into a
prismatic form, each ball constituting a separate joint in the
basaltic massf."

Dr Daubeny supposes that in this case the molten lava had
been free to flow partly away from among the supposed globular
concretions during the time of their solidification and growth, and
that thus the supposed globular structure had room freely to
develop itself — the surrounding vacancies affording to the balls
freedom from much compression, and leaving them free to retain
their original globular figure J. Dr Daubeny contrasts the com-
pact prismatic columns at Fingal's Cave at StafFa with the columns,
resembling piles of nearly globular cheeses, in this German cave ;
and accounts for the difference by supposing that the basalt of
Staffa was solidified as a continuous bed without there having
been freedom for the molten lava to escape from among the
supposed balls during their supposed solidification and growth ;
and he attributes the hollowing out of the Staffa cave in the solid
columnar rock to the action of the sea, while the Kase Keller was,
he believes, an original cavity in the rock whilst still hot and only
partially solidified — a cavity formed by the flowing away of liquid
basalt from among the supposed piles of globular concretions. In
closing his discussion of the subject, Dr Daubeny distinctly
announces, as the conclusion he arrives at, " that the spheroidal
structure will be found to be one of the most prevalent in rocks of

This drawing of the Kase Keller is copied from one in Lyell's Manual of
Elementary Geology, 3rd edition, 1851, p. 386, as that seems to be a better drawing
than the sketch at p. 79 in Daubeny's book.

t Daubeny, p. 78. + Daubeny, p. 78.

426

GEOLOGICAL

[62

Fig. 1. Ease Keller.

Fig. 2.

Fig. 5.
Mary II . Thomson, del.

Fig. 6.

Fig. 3.

Fig. 4.

Fig. 7.

1877] ON JOINTED PRISMATIC STRUCTURE IN BASALTIC ROCKS 427

the trap family, and that the prismatic structure is in general only
a consequence of the spheroidal *."

The views put forward in detail by Dr Daubeny have here been
briefly cited, as they constitute a fair enough specimen of the
general character of views offered, though with many variations,
by different geologists of note. Mr Scrope, however, repudiates
the spheroidal concretionary theory, denying that the columnar
structure could have had its origin in spheroids pressing against
each other, pointing out, that imbedded knots of olivine are often
to be found severed apart by the seam which separates two con-
tiguous columns ; and he thence argues, " that it is impossible to
talk any longer of the columnar structure being occasioned by the
mutual pressure of spherical concretions f." He then himself
maintains that the columns have originated through " fissuring "
of the hot rock by " contraction " during its process of " con-
solidation " or " refrigeration," and he supposes the cross-joints
to have been formed contemporaneously at each part of the
length of the column with the advance of the prismatic
fissures J at that same place, the cross-joints being supposed
to be successive bounding faces between the solidified end of
the column and the as yet molten lava into which the solidi-
fication is advancing, and the prismatic fissures being supposed
at each period to extend quite forward to the molten lava§.
Mr Scrope's view, as he himself states in the passage referred to,
comprises the supposition that the concavity of the ball-and-socket-
like cross-joints ought to be always directed upwards — that is,
nearly in his own words, in the direction facing away from the

* Daubeny, p. 661.

t See citation from Scrope in Daubeny's second edition, page 65, note. (A
passage nearly to the same effect as this citation is to be found in Scrope, Volcanos,
revised and enlarged second edition of date 1872, pages 103 and 104, foof note.)
Daubeny, in his passage just referred to, follows up his citation from Scrope about
the knots of olivine by dissenting from Scrope's conclusion, and still maintaining
that the columns have been formed by spherical concretions which, while forming
themselves by mutual pressure into columns, would be still in a soft and pasty
state ; but asserting that the seams or severances between the columns, and cutting
through the knots of olivine, might take place by shrinkage after consolidation.
The general tenor of the arguments in the controversy between Daubeny and
Scrope exhibits strikingly an utter bewilderment pervading the minds of both on
this subject.

£ Scrope, Volcanos, 2nd ed., 1862, page 104.

§ Ibid. Much, if not all, of the same remains in Scrope, revised and enlarged
second edition, 1872.

428 GEOLOGICAL [62

surface of refrigeration, which he believes to be uniformly the
bottom or base of the lava bed; or, in other words, that each
separate piece of the jointed column ought, according to his
supposition, to have its bottom convex and its top concave. This
supposition, the author (Professor Thomson) remarks, is not veri-
fied, but is decidedly controverted by the basaltic columns of the
Giant's Causeway, the cross-joints being often concave upwards,
and often concave downwards, and often nearly flat : and this one
circumstance, even by itself alone, Prof. Thomson considers must
set aside the suppositions maintained by Mr Scrope. That the
cross-joints as exposed to view in the Giant's Causeway are some
of them convex upwards, and some concave upwards, is very
clearly shown in Figs. 8 and 9, which are accurately copied from
excellent photographs selected by the author on a visit to the
Causeway when he was scrutinizing the stones themselves, and
found the photographs to give good representations of various
features important for the geological considerations under dis-
cussion in the present paper. It may be noticed, that in each of
these two drawings some of the exposed joints forming the tops of
the columns left remaining are convex upwards, and that others
are concave upwards ; and that some of the concave ones in Fig. 9
are distinctly indicated by their having rain water lying in their
hollow tops.

Professor Thomson then gave a discussion of the spheroidal
concretionary theory. He showed many objections to it, any
one of which separately, he said, might be sufficient to set it
aside. He believes it to be founded from the outset on a total
mistake. He regards the spheroids so often met with in decaying
basalts or lavas as being not concretions at all, but as being the
results of decay or decomposition penetrating from without inwards
in blocks, into which the rock has been divided by fissures, which
may have arisen from various causes. Examples of such spheroidal
exfoliations are shown in Figs. 2 and 3, p. 426. Fig. 2 is a
drawing from an actual stone picked up on a hillside, and which
may be assumed to have been long exposed to weathering. The
stone itself when scrutinized shows at least six distinct shells or
coats surrounding a nucleus. Fig. 4 is given as a drawing from
Prof. Thomson's own observations of exfoliation proceeding inwards
in blocks of shattered trap noticed in situ in a quarry near Largs,
or of exfoliation such as may often be seen elsewhere in shattered

1877] ON JOINTED PRISMATIC STRUCTURE IN BASALTIC ROCKS 429

Fig. 8.

Mary H. Thomson, del.

Fig. 9.

430 GEOLOGICAL [62

basaltic or trap rocks in situ ; and as indicating clearly that the
positions of the several foliations and nuclei are determined, not
by any original concretionary action, but by the casual cracks pro-
duced, it may be supposed, by earthquakes at various times. In
reference further to the concretionary theories of basaltic columns,
he pointed out that even if concretions were forming in a
cooling mass of molten basalt or lava, we have no right to
suppose that they would arrange themselves in straight, or
nearly straight, rows, like beads on a vast number of parallel
strings ; nor that, if they did exist, and were so arranged, those
in any two adjoining rows would so meet as, in pressing Against
each other, to form continuous columnar faces ; and he gave
various other reasons, though those here cited may amply
suffice. He believes that no credence whatever ought to be
given to any form or modification of the spheroidal concretionary
theory of the jointed prismatic structure, but that it ought to be
utterly and promptly rejected from the science of Geology, without
any vestige of it being retained to confuse the investigation of the
subject in the future.

Professor Thomson proceeded to give his own theory, which
may be briefly sketched out as follows : — He supposes that
the division into prisms has arisen by splitting, through shrink-
age, of a very homogeneous mass in cooling, and thus far his
explanation is in agreement with parts of the views of some
of those who have previously speculated on the subject. Beyond
the mere attribution of the mode of origin of the prismatic
columnar structure to splitting through shrinkage in cooling, like
the cracking which may be observed in starch or mud in drying,
he offers some explanations as to what conditions, affecting the
stresses in the interior of the mass, and involving the influences
of contemporaneity or of sequence in time of different parts of the
fissure system, must accompany the progress of the system through
the interior of the mass. He shows how the splitting action in
the interior is distinct in essential features from any such cracking
as is exhibited on the surface of mud in drying, and from the
cracking into a tesselated pattern, of the glaze on porcelain, or of
the varnish on terrestrial or celestial globes. On this subject,
briefly mentioned at this stage, his remarks will be cited more
fully further on in the present abstract. He thinks there yet
remains ample scope for much additional scrutiny, both observa-

1877] ON JOINTED PRISMATIC STRUCTURE IN BASALTIC ROCKS 431

tional and theoretical, towards fuller elucidation of the conditions
accompanying the remarkable results presented by the prismatic
structure often met with in basaltic and various other rocks, and
other substances.

The "cross-joints," he specially remarks, are in no way es-
sential to the formation of the prismatic structure; for the
columns are not always jointed, but are sometimes found quite
continuous for lengths great relatively to their diameters, so as
to constitute long bars of stone. In excavations, for instance,
which were made for the formation of the new Cemetery at
Belfast, columnar structure in basalt or other trap rock was met
with, the columns being often many feet in length, and only a
few inches in diameter. Fig. 5, p. 426, shows a portion of one
of those long columnar bars which were devoid of the so-called
cross-joints.

The chief new view, which had originated with himself in
connection with this subject, and which he offers as a contribution
towards the development of any true theory, depends on a supposi-
tion which had occurred to him in August, 1861, through careful
scrutiny and consideration of appearances presented by stones in
the Giant's Causeway. This supposition is that the so-called
" cross-joints " are fractures which have commenced in the centre
of the column, and have advanced to the outside as a circle
increasing in diameter. This mode of fracture, he thinks, is
evidenced by various markings which he has specially observed in
many stones of the Giant's Causeway. These stones usually show
a remarkably symmetrical conformation round the outer parts of
their cross-joint faces, a conformation which has commonly been
associated in idea with ball-and-socket jointing, and has often been
attributed to spheroidal concretionary growth ; but which to him
had presented appearances [see Figs. 6, 8, 9, 10, and 11, pp. 426,
429, 435] suggestive of a connection, in nature and mode of
origin, with those appearances which are remarkable in an ordinary
conchoidal fracture — subject to the important distinction, however,
that while the conchoidal fracture, in ordinary cases, has emanated
from an external spot of the stone where the blow has been struck,
the supposed conchoidal fracture across the column appears to have
started into existence at the centre, or at some internal spot in
the column, and to have flashed thence with a complete circular
advancing front towards the exterior of the column. The kind

432 GEOLOGICAL [62

of fracture thus imagined may be briefly designated as a circular
conchoidal fracture.

On the cross-joint faces, or surfaces of transverse partition, in
numerous instances he has noticed roughly figured rays spreading
out from or converging towards the centre or some other internal
spot in the face. These appeared to him, from the time of his
first observing them, in or before 1863*, to be of the same nature
as the well known fan-like radial markings of a conchoidal
fracture.

Following up the train of consideration and scrutiny thus
suggested, he remarks that there are not many very distinct ways
in which we can suppose a fissure to have spread across a column
or prism of solid stone. First, if we for a moment suppose the
fissure to have begun at one side of the column, and to have
advanced across to the opposite side, we must expect to find the
resulting fracture quite unsymmetrical, and presenting very
different appearances at the places where it entered the previously
unbroken stone prism, and where it came to its termination,
leaving the column broken behind its advancing front. No such
appearance is to be found in any of the ordinarily shaped cross-
joints; but, on the contrary, there is commonly a very remarkable
appearance of approximate symmetry of character in the cross-
joint with respect to the different sides and angles of the column.
Perfect symmetry is, of course, not to be expected, as the columns
themselves are often far from being of any regular or symmetrical
form ; but, so far as Professor Thomson's observations of the stones
in the Giant's Causeway have extended, he believes no appearance
is to be found indicating an advance of the fissure across the
column from one side to the opposite, in any of the joints which
exhibit, in other respects, the usual remarkable features. There
may, no doubt, be numerous cases of fracture due to shattering,
by causes different from those which have produced the ordinary
remarkable transverse severances. Next, any idea that the
cracking of the column could have simultaneously begun all round
the circumference, and advanced to terminate in the centre,
requires little more than to be brought before the mind for
consideration to be rejected as untenable. There seems, then, to

* Mention of these rays as noticed by the author is to be found published in
an abstract of a paper by him, in the British Association Report, Newcastle
Meeting, 1863, p. 89 of part 2 of the Report.

1877] ON JOINTED PRISMATIC STRUCTURE IN BASALTIC ROCKS 433

remain nothing to suppose but that the ordinary cross-joint
fissures first came into existence in the interior of the column, and
then flashed out thence towards the circumference.

In order to produce the cross fractures commencing in the
centre, he supposes that a longitudinal tensile stress must have
existed in the middle of each column previously to the cracking
of the cross-joints. To account for such a tensile stress, he
suggests, as a probable hypothesis, that after the column was
formed, chemical action, caused by infiltration of water, might
cause an expansion of the outside of the column, and that the
outer part, thus growing longer, would pull the internal part more
and more intensely, until at last the internal part would give
way, and break into short lengths. The fissures thus formed, it
is obvious, must stop short without extending quite to the outside
of the column, as the pull causing the fracture in the interior is
due purely to longitudinal push in the outer part of the column.
That outer part, therefore, will not be subjected to the pull at all,
and so the enlarging circular conchoidal fracture should be expected
to stop short without penetrating to the outside of the column,
especially at the angles. On the event of the central part cracking,
and so ceasing to bear a pull, the outer part, being less resisted
than before, would increase in length in the immediate neighbour-
hood of the new internal fissure, and so would bring parts nearer
the circumference than before into the condition of being subject
to a pulling stress. Also, the reverberation or tremor at the
instant of the cracking might, it seems reasonable to suppose,
carry the advancing circular edge of the fissure somewhat further
out than the region which would be subjected to a pull if the
action were slow instead of being by a start. The appearances of
the cross-joints — with the central area of each like a circular or
oval flattish face, or like the convex or concave form of a watch-
glass, but not extending out quite to the angles, and usually not
quite out to the sides of the columns — seem to be in accordance with
the suppositions here made, and to give considerable corrobora-
tion to them (see Figs. 6, 8, 9, 10, and 11).

The cracks, if formed as supposed, without extending quite to
the outside of the column, would constitute places of weakness,
from which, under the shattering influence of earthquakes or other
causes, fresh fractures would readily proceed quite to the outside,
severing the columns completely across ; but these fresh fractures

T. 28

434 GEOLOGICAL [62

occurring in ways quite different from those in which the original
circular ones had done, could not be expected to be in continuity
with the supposed original circularly terminating fissures. Thus
is accounted for the approximately circular outer boundary to the
flattish or lunette-shaped middle part of the cross-joint, which is
very commonly to be seen.

On a visit to the Giant's Causeway in the summer of 1869,
Professor Thomson had noticed some phenomena tending to
confirm his previously formed views. He met with several
instances in which a small mass of stone, different in texture and
in hardness from the rest of the basalt, showed itself in the cross-
joint of the column, and in which the joint presented to his view
the appearance as if the cross fracture had originated at, and
spread out from, this spot of irregular quality. When this
extraneous or irregular lump happened to be near the middle of
a column, there appeared to emanate from it in all directions
approximately straight but roughly formed rays (see Fig. 10,
and Fig. 8, with the explanation in footnote)*; and when the
lump happened to be near one side of the column, the rays
emanating from it spread out in curved forms like a brush,
and the several rays in proceeding outwards seemed to bend
gently somewhat towards the nearest external face of the column
(see Fig. 11, and its explanation in footnote)")". This seemed
as if they had tended to run so as at each moment to be

* Fig. 10 shows the general character of features frequently to be noticed
with approximately straight rays emanating from about the centre of the column.
In this figure, in one or more of the columns, a nucleus or lump of a different
kind of stone is shown in the centre, in imitation of what has been noticed by
the author in several cases in which a distinctly observable nucleus appeared
to him to have originated the fracture. Fig. 8 is accurately drawn from a
photograph of the group of stones ordinarily shown by the Causeway guides to
visitors as the " Ladies' Wishing Chair." Of the columns here shown the one at
the left front of a person sitting in the chair shows faintly in the figure, but shows,
or at least when last seen by the author, did show very distinctly the appearance,
on its top, of radiating striae or roughly formed rays, which seemed to betoken a
conchoidal fracture.

f Fig. 11 is copied accurately in outlines and all essential features from
a drawing of an actual column in the Giant's Causeway. The original drawing
was made by the author (Professor Thomson), not from memory, but while standing
over the stone, and imitating carefully all the main features. The nucleus from
which the brush emanates was of a very hard, dark-coloured stone. The original
of this drawing he has carefully preserved for security against casual development
of modified features in the making of copies.

1877] ON JOINTED PRISMATIC STRUCTURE IN BASALTIC ROCKS 435

Fig. 10.

Fig. 14.

Fig. 13.

Fig. 16.

Fig. 17.
Mary H. Thomson, del.

Fig. 18.

28—2

436 GEOLOGICAL [62

advancing in a direction approximately perpendicular to the
advancing circular or oval edge of the enlarging fissure. If
a fracture originating at one side of a column were to advance
across to the other side, and in so doing were to cut across
any irregular lump in the mass, that lump would leave a kind
of tail extending from itself forward in the direction of pro-
pagation of the fissure; but the part of the fissure formed
before arrival of the fissure's edge at the lump would be scarcely
at all influenced by the presence of that irregularity. A tail
emanating in this way from an irregular lump or a vesicular
cavity, and extending forward in the direction of advance of
the crack, is continually to be noticed in the breakage of flints,
glass, basalts, and other brittle substances. Now, the cases
noticed at the Giant's Causeway, in which, from an included
lump, the lines radiated out in various directions, and were curved
when the lump was eccentric, tend to corroborate the supposition
that the fissure had its beginning at the irregular lump, where
some local weakness or overstraining might exist, and that it
flashed out from thence towards the circumference of the column.
He mentioned that, in favour of his supposition of possibility of
a crack commencing at some central point, and diverging outwards
with an enlarging circle as its front or edge, so as to constitute a
circular conchoidal fracture, a remarkable confirmation had, long
after the publication of his views as to the nature of the cross-
partings in basaltic columnar structure, presented itself to him in
the features of a broken flint found casually in a heap of broken
stones. This flint, which he showed at the meeting, is represented
in Fig. 12. The appearances presented by this piece of flint,
in its cone with divergent rays, lead to the belief that it must
have received the remarkable conical part of its configuration
through a blow struck, on an originally larger mass of flint, at the
spot where there is now the vertex of the cone; and that, from the
point of impact, a fissure must have flashed out in conical form,
with a divergent or expanding circle as its advancing front or
edge. That any uncrushed material should remain at the place of
violent impact to form the smooth point of the cone, might be
thought scarcely credible ; but confirmation as to this supposition
is to be obtained through noticing divergent cracks, which may
occasionally be seen in solid glass balls used as children's playthings,
like boys' marbles. These balls, after having been knocked about,

1877] ON JOINTED PRISMATIC STRUCTURE IN BASALTIC ROCKS 437

sometimes show cracks, with circular margins, penetrating into the
interior from points of impact, and which may be characterized,
along with such as the one just referred to in the flint, by calling
them conical conchoidal fractures. These fractures have re-
semblance in shape to limpet shells. An example of these
in the glass balls he showed at the meeting, as also another
broken flint, which he had subsequently found, showing a
like conical feature to that of the one first noticed, and in-
dicating that the first one is not to be regarded as an isolated
result of casual circumstances unlikely to recur ; but that there
must exist some tendency, or readiness, to the formation of such
fractures emanating from spots of violent straining in some cases
of impact.

He adduced another confirmation of his view as to the cross-
partings in the columns — a confirmation which had been found
and carefully considered by Mr W. Chandler Roberts*. It was in
a piece of indurated clay or red ochre that the confirmatory
phenomena were met with. Mr Roberts, when on a geological
excursion to the Giant's Causeway, at the close of the Belfast
Meeting of the British Association in 18V4, just after attention
had been freshly brought to bear on the subject by papers read by
himself and the author at that meeting, happened to find the
piece of red ochre, and was struck with its features as being
remarkable in their resemblance to those specially noticed under
the views of Professor Thomson in regard to the cross-partings in
basaltic columns. Mr Roberts carefully preserved the specimen,
and, by his kindness, Professor Thomson was enabled to show it
at the meeting of the Glasgow Geological Society ; and it is well
represented in Fig. 13, p. 435, where it is shown on a slightly
enlarged scale, the lineal dimensions being increased to about 1£
of the corresponding lengths in the little block of ochre itself,
which is of a roughly cubical form, and about the size of a hazel
nut. One face of this little block shows very remarkably the same
kind of features as those which, met with in basaltic columns,
are specially brought into notice in Figs. 10 and 11, p. 435.
There is a speck or granule from which, as it appears, a divergent
circular conchoidal fracture has originated; there is a lunette-
shaped portion bounded by a circular or somewhat oval margin,
where some delay or vibration in the propagation of the advancing
* [Deputy-Master of the Mint — afterwards Sir Wm. Roberts-Austen.]

438 GEOLOGICAL [62

fissure may be supposed probably to have occurred, and to have
left its mark. Outside of this margin, very distinctly marked,
radiating, brush-like striae are situated, and these seem to show
that, after some delay or modification which left the oval margin
marked, the fissure had continued to advance outwards. This
wonderful miniature occurrence, seemingly of the same kind of
fracturing process as appears to have occurred in a large way and
with multitudinous repetition in the rock of the Giant's Causeway
itself, is not to be supposed to have any special connection, in virtue
of locality, with the basaltic structure there. The little block
of ochre, though found near the Causeway, is not to be supposed
to be part of a tiny column, such as those of the Causeway, and
due to the same set of localized causes. Its occurrence there, and
its discovery there, must be attributed merely to casual coincidences.
In respect to the manner in which the fissuring of the rock
longitudinally into columns may be supposed to have occurred,
the author drew special attention to distinctions in the circum-
stances, on the one hand, under which a tesselated system of
cracking can spread out over an extensive surface of rnud in
drying, as in cases when the water is drawn off from a pond
having a smooth, muddy bottom, or under which tesselating cracks
often spread over the surface of the glaze of porcelain, or over
the varnish of terrestrial or celestial globes ; and on the other
hand, under which a fissure system can penetrate with columnar
configuration through the interior of a mass of rock. In the
spreading of a system of tesselating cracks over a surface of
shrinking mud, or over the glaze of porcelain — which, probably
by penetration of moisture, or from some other cause, may be
supposed to swell more than the film of glaze on its surface can
endure — or over the varnish of a globe, it is usually to be noticed
that a few long and often approximately straight or moderately
curved fissures first break out, and that other fissures break
transversely to them, but generally or always stop on abutting
against any previously formed fissure ; and that the subdivision
or tesselation may, by successive transverse cracks, each stopping
against a previous one, be carried on more and more. This is
exemplified in Fig. 14, p. 435, where the order of sequence of
the successive breakages in many cases can readily be judged of
by noticing that, when one crack abuts against another, which
extends continuously across the point of abutment, the abutting

1877] ON JOINTED PRISMATIC STRUCTURE IN BASALTIC ROCKS 439

one is the posterior of the two. This kind of tesselation is, how-
ever, very essentially distinct from that which is to be seen in
walking over the Giant's Causeway, or in examining the con-
figuration of basaltic rocks in general. In the tesselation occurring
in basaltic rocks (see Fig. 17, p. 435), we never find any of the
regularly formed fissures of the column side faces abutting against
any fiat column face. No such configuration is met with as is
sketched in Fig. 18. Wherever a separating fissure between two
columns meets another column, at that place there is an edge or
arris line of meeting of two faces of that other column — that is
to say, that regularly or ordinarily three fissures separating three
columns radiate out from one common arris line for all the three
(see Fig. 17, also Fig. 16). It seems that even if, from any cause
— as, for instance, in the case of a mud surface in drying — there
were formed a long, straight, or curved crack, such as LM, Fig. 15,
and if another crack, cd, were to terminate against it, as at" d,
the part ab being straight or curved, a change -would take place
during the inward advance of the fissuring into the body of the
mass, under which ad and db would cease to be continuous,
and would come to form an angle, adb, somewhat as shown in
Fig. 16.

He called attention to a class of facts which within recent years
had been brought prominently into notice in connection with
opinions which may or can be held regarding the mode, or possibly
varied modes of formation of columnar structure in rocks. Mr
W. Chandler Roberts, at the Belfast Meeting of the British
Association in 1874, had pointed out that a prismatic structure,
closely resembling that of basalts, can be produced artificially at
will in certain brick-like masses of fire-clay and sand, by heating
them under certain conditions to redness — a temperature far below
that at which they would fuse. This indicated still more strikingly
than had previously been done by the columnar cracking of starch^
and some other substances not molten, that a process of cooling
from the molten state is not at all essential to the formation of
columnar structure resembling that of basalts. In the case of
basalts, undoubtedly, cooling from the molten state has occurred,
and we may suppose that the columnar fissuring took place at some
stage in the process of cooling.

He also referred to the existence of columnar structure in
sandstones, which had recently been brought into notice among

440 GEOLOGICAL [62

geologists in a paper by Mr David Corse Glen, F.G.S., printed in
the Society's Transactions, Vol. V., p. 154, 1873, relating chiefly to
columnar sandstone at Kilchattan, in the island of Bute. In the
development and discussion of theories as to the columnar structure
in basalts, previously to this paper by Mr Glen, the existence or
columnar structure in sandstones had, so far as Professor Thomson
knew, been quite unnoticed ; and, if at all mentioned, he believed
had not been introduced in any important way into consideration.
The notion of the columnar structure having instituted itself by
some concretionary or other action within the material undergoing
solidification, but barely solidified from the molten state, had
indeed commonly exercised a too dominant influence in the con-
sideration of the subject. It is important to notice that the
sandstone columns of Kilchattan, in Bute, are quite devoid of any
such cross-jointing, or cross-parting, as that which is remarkable in
the columns of the Giant's Causeway. The longitudinal direction
of the columns is nearly vertical, and they cross the planes of
stratification obliquely at an angle of about 60°. Their direction
and configuration seem to have been determined quite independently
of the stratification. Fig. 7, p. 426, is a drawing of a portion
taken from one of these sandstone columns of Bute. The strata
show themselves passing obliquely across the column, being dis-
tinctly indicated through varieties of colouring and grain; and they
are represented in the drawing. This column is about five inches
in diameter; and the set of columns are stated by Mr Glen as
varying in size from six or seven inches diameter down to half an
inch. The manner in which these columns have originated, and
the circumstances which have determined their sizes, or some
average sizes which they might tend to assume rather than other
very different sizes, must remain as important, and probably as
very difficult, matters for research and for theoretical speculation.

MISCELLANEOUS PAPERS

63. ON ATMOSPHERIC REFRACTION OF INCLINED RAYS,
AND ON THE PATH OF A LEVEL RAY.

[From the Report of the British Association, Section A,
Brighton, 1872, page 41.]

MANY years ago, in considering, from a civil-engineering point
of view, the path of a level or nearly level ray of light through
the atmosphere, with special reference to corrections in observations
with the levelling-instrument, the author found himself unable to
rest satisfied with the views put forward on the subject in books
on Practical Geodesy, or in any writings with which he was
acquainted. The only views which he then met with were to the
following effect : —

The atmosphere was regarded as consisting of an infinite
number of infinitely thin horizontal laminae, with a gradual
increase of density in passing downwards through these laminae,
so that the density in each lamina would differ only in an in-
finitely small degree from that in the one immediately above it, or
from that in the one immediately below it. It was then inferred
that a ray of light, passing obliquely downwards through the
laminae, must, at each successive transition from one lamina into
the denser one next below, suffer refraction so that its course must
make a less angle with a normal to the laminae in the denser
lamina than it did with the same normal in the rarer one im-
mediately above, and that the path of the ray must therefore
be curved with the concave side downwards. From this reasoning,
without noticing that its whole foundation, in oblique transition of
the light across laminae with gradual change of density in those
successively traversed, vanishes in the case of a horizontal ray,

442 MISCELLANEOUS PAPERS [63

authors have tacitly assumed that a ray proceeding through the
atmosphere, so as to enter a levelling-instrument horizontally,
should be expected to be curved with its underside concave. In
one sense such a conclusion, in connexion with the mode stated in
which it has been inferred, may be partly justified — that is, if the
consideration be that a ray coming from a considerable distance so
as to enter an instrument horizontally must have previously been
descending obliquely through the nearly spherical level laminae of
the air which are rounded in correspondence with the figure of the
earth. Rays arriving level at an observer's station from the rising
or setting sun afford an instance of what is here referred to, and
one in which the light has descended obliquely through the whole
depth of the atmosphere. It may readily be admitted, from the
usual reasoning cited above, that any such ray will be curved and
concave downwards at all parts of its course where it is sensibly
descending ; but as the advancing ray gradually approaches to the
level position with a gradual diminution down to cessation of
oblique descent through the laminae, it might still, so far as that
reasoning would indicate, be held an open question whether the
curvature of the ray would approach towards zero, or whether it
would approach towards a maximum, or generally what might be
the condition as to curvature or straightness of the ray, as the ray
comes to be level.

The author proposed the question in 1863 to Professor Purser,
of Queen's College, Belfast ; and Prof. Purser, on the moment,
made out an analytical investigation which depended on the
proportionality of the sine of the angle of incidence to the sine of
the angle of refraction holding good for infinitely thin laminse
differing infinitely little in density, and holding good to the extreme
case in which the ray becomes parallel to the laminse. This
investigation appeared to the author of the present paper to be
consistent with all physical conditions ; and he regarded it as an
hypothesis likely to be fully confirmed by experimental investiga-
tions, if at any time experiments bearing on the subject should be
found practicable. From direct experiments, however, on the
curvature of a ray of light in the atmosphere, no accurate results
are to be hoped for, on account of the great and constantly varying
disturbances to which the ray is subject, through changes in the
distribution of heat and moisture in the air, and movements of its
parts among one another, and other varying influences.

1872] ATMOSPHERIC REFRACTION 443

Prof. Purser's investigation, which from the first has been
deemed by the author of the present paper to be of much interest
and value, was to the following effect, the question being: —

To find whether a ray of light passing infinitely nearly horizon-
tally through the atmosphere will be bent with a finite curvature, or
not bent at all ; and whether the curvature approaches to a maxi-
mum or to a minimum as the direction of the ray approaches
towards horizontality.

Conceive two laminae, Lamina 1 and Lamina 2, each of the
thickness X. Conceive the density in each
as being constant, but that there is a sudden ~

increase of density in passing from the one

to the other. Then the ray of light PA 0 2 ^

will at A be suddenly bent or deflected o

from its previous line. This case may be

substituted mathematically, when the laminae are taken infinitely

thin, for what actually occurs in the atmosphere.

Now in the atmosphere the deflection of the ray of light
in passing from the middle of one lamina to the middle of the
next, as from D to E, is evidently proportional to the thickness
assumed for the laminae, the thickness being small. Hence, if we
take 8 to represent the angle of deflection at A, we must bear in
mind that & oc X for any given angle of incidence, or that 8 must
be infinitely small when the lamina is infinitely thin. Let the
angle of incidence PAB = i. Then, by the ordinary law of
refraction assumed as applicable to this case,

sin i = IJL sin (i — 8),

in which //, denotes the index of refraction for passage of a ray
from one lamina to the next when the thickness of the laminae is X.
m TI ?

Hence - — = sin i cos 8 — cos i sin 8, or by dividing by cos i,

tan i • * • *

- = tan i cos o — sin o.

P

But 8 must be infinitely small, the laminae being infinitely thin.
Hence for infinitely thin laminae we have sin 8 = 8, and cos 8 = 1.
Hence the previous equation becomes

tan i . ~

- = tan i — 8,
P

LL-l

or 8 = - tan i.

444 MISCELLANEOUS PAPERS [63

Let DE, or its equal PA, the laminae being infinitely thin, be
denoted by s. Then s = \ sec i.

Let the radius of curvature of the ray of light, or the radius
of the circle touching the ray in the points D and E, be denoted
by R, and then we have

Curvature = ^ = - .
H s

fji—\ tan i

Hence Curvature = — . ,

fji\ sec ^

• •*

or Curvature = — —sin i.

p\

But since the curvature of the ray of light is independent of

the small thickness which we may take for the infinitely thin

laminae, and can only vary with the angle of incidence i, we must

have IJL — 1/yttX in the foregoing equation constant ; and so we have

Curvature or sin i,

which has its maximum value when i is a right angle ; that is,
when the ray is passing horizontally, or infinitely nearly so.

This shows that if the ordinarily assumed law of refraction
be truly applicable to a ray of light passing extremely nearly
horizontally through level laminae of air of varying density, the
curvature of the ray of light must approach to a maximum as the
inclination of the ray approaches to horizontality. From this, if
true, the step is natural, or inevitable, to the conclusion that,
leaving out of account the rotundity of the earth, and conceiving
the laminae of constant density to be level planes, a ray of light
directed level so that if it were to traverse a straight path it would
pass along an infinitely thin lamina of uniform density, but with
less density above and greater below, would be bent by virtue
of the difference of the densities above and below it.

It must, however, be admitted that there is something per-
plexing, or not quite satisfactory to the mind, in taking this final
step to the perfectly level ray ; for as soon as the inclination of the
ray becomes zero the whole foundation and framework of the
investigation fails, there being then no oblique passage of a ray
from one lamina into another, no incident and no refracted ray,
and consequently no ratio of sines of angles of incidence and
refraction ; though all -these would be required to be discussed as

1872] ATMOSPHERIC REFRACTION 445

if they existed in the case of every ray whose curvature is to be
compared with that of any other. Still, as both Professor Purser
and the author thought at the time, the investigation made the
physical conclusion as to level rays seem highly probable ; since, if
it proves, as it seems to do, that a ray of light descending obliquely
must move along a certain curved path, and that the curvature
must increase as the inclination approaches towards horizontality,
and also that the rate of change of curvature with change of
inclination approaches towards zero as the inclination approaches
towards horizontality, it must follow that a ray of light passing
exactly level will be bent with the same curvature as one infinitely
nearly level.

Several years later (in February 1870) a new investigation
occurred to the author of the present paper. The new one is
much simpler, and it is more general, and its reasoning holds good
alike for level as for inclined rays. In fact the previous investiga-
tion, founded on the ratio of the sines of angles of incidence and
refraction, and therefore in principle having no direct applicability
to level rays, comes, when considered in connexion with the new
one, to be a case of this more general one, seeing that under the
undulatory theory of light the proportionality of the sines of the
angles of incidence and refraction is not an ultimate fact or
principle, but a consequence of retardation of the velocity of light
in the denser medium. In the new investigation which will now
be submitted the retardation of the velocity of light in the denser
medium is taken as the basis of the reasoning.

Let MN and OP be two level surfaces in the atmosphere, and
let each of these be supposed to pass
through air of uniform density through-
out each of them. They may be con-
ceived to be at a very small distance
apart, and then obviously a ray in de-
scending obliquely from one to the other
will alter its curvature only by a very
slight amount, *\

The fundamental assumptions on which \

the investigation will be based are the \

following three : —

(1) It is assumed that the light at
A has a certain velocity, which may be Flg' 2'

446 MISCELLANEOUS PAPERS [63

called vlt and that the light at B, where the air is denser, has
a smaller velocity, which may be called v2.

(2) It is assumed that these velocities are constant for all
inclinations of the ray of light ; or, in other words, that the
velocity of the ray of light is independent of the inclination of the
ray to the horizontal strata of the air.

(3) It is assumed that the direction of the light is per-
pendicular to the wave front, or that a surface taken crossing
every ray in a pencil of rays perpendicularly, and then conceived
to advance along the course of each ray with the velocity of that
ray, will continue to cross every ray perpendicularly.

Now let AB and CD be two successive positions, indefinitely
near to each other, of the advancing front of a ray or pencil of
light whose direction of advance is indicated by the lines EA and
FB, and by the arrows R in the figure, the direction at all points
of AB being normal to the plane represented by AB. Let the
inclination of AB to the vertical line BH be denoted by 0, which
will then also denote the inclination of the ray to the horizon.
Let the thickness of the lamina of air from MN to OP be denoted
by X, or let BH in the figure be denoted by X.

The lengths A C and BD have to one another the same ratio as
the velocities of light at A and B respectively ; or

AC : BD :: v, : v,.

If A B and CD be produced till they meet in G, the length GA
is the radius of curvature of the ray at A. Let this radius be
denoted by r. Then, since AB is = X sec 0, we have obviously

v1 — v2 : vl : : X sec 0 : r.
Hence curvature or

1 v - v.

. cos t/,

or curvature oc cos 0 ; which shows that the curvature is a maxi-
mum when # = 0, that is, when the ray is level, and that the
curvature diminishes to zero as the ray becomes vertical.
The result here brought out,

is perfectly in agreement with that arrived at in the previous

1872] ATMOSPHERIC REFRACTION 447

investigation of Prof. Purser, namely - = — — sin i, seeing that

T fJ,\,

sin i is = cos 0, and that, according to the undulatory theory of
light as confirmed by experimental proofs, it is known that

v.iv^.ifji: 1,
so that 1 2 must be equal to . The new method has

V, IL

however, the advantage of quite clearing away the perplexity
involved in the other by the collapse of the reasoning when
brought to the extreme case of the level ray. In the new method
no such collapse occurs ; and, in fact, the new method shows clearly
how the real fundamental principle (that of retardation of velocity
in the denser medium, on which the bending depends, and which
holds good quite as much for level rays as for any others) is allowed
in the previous investigation gradually to fade out of the reasoning,
till, in the case of the level ray, it has absolutely vanished from
the conditions which were taken into account. The previous
method, like the modes of considering the subject of atmospheric
bending of rays which appear to have been most generally
entertained hitherto, took a consequence of the important funda-
mental principle into account instead of the principle itself (that
consequence being the proportionality of sines of angles of in-
cidence and refraction in case of oblique transition of light from
one lamina to another of different density) ; but that consequence
happens to be not so general as the principle from which it follows,
and to be one which becomes nugatory or non-existent in the case
of the level ray.

In concluding, the author wishes to state that it seemed to him
rather unlikely that so simple a view of the influence of the
atmosphere in effecting the bending of rays of light as that which
he has now offered could be quite new. He thought that others
better acquainted with the science of light than he is must most
probably have entertained the same or similar views. He has
therefore made inquiries as to the views which have hitherto been
put forward regarding the bending of light in the atmosphere and
in other mediums of continuously variable index of refraction, or,
as they may be better considered in the present investigation,
mediums of continuously varying light-velocity*. Much has been

* fjr1 might be called the index of light-velocity.

448 MISCELLANEOUS PAPERS [63

written on the subject in general, and on various particular cases
of its application ; and views very similar in principle with those
here offered appear in various ways to have been entertained,
or implied more or less explicitly ; but he has not learned of any-
thing having been taught which has anticipated the treatment of
the subject at present offered so as to deprive it altogether of
novelty and interest. The subject, he believes, has been very
generally considered under imperfect views; and he will think
a good result will have ensued if his drawing the attention of the
British Association to it will serve to elicit from others notice of
the best views that have hitherto either been fully published,
or have been entertained or discussed without complete publi-
cation.

POSTSCRIPT. — From Professor Clerk Maxwell I have learned
that, in December 1851 or 1852, when on a visit to my brother,
Sir William Thomson, he had in his mind the consideration of the
path of rays in a medium of continuously variable index of
refraction ; that he then thought it easiest to calculate the path of
the ray by translating the problem into the emission theory, and
treating the ray as a moving body acted on by a force depending
on the variation of the index of refraction, and so proceeding
by an artifice justifiable on the ground that the emission and
undulation theories are mutually equivalent in respect to the
course of rays when the proper alterations of the hypotheses are
made ; and that my brother showed him, on the other hand, how
easy it is to begin with the right hypothesis by making the
velocity inversely proportional to p, and calculating the change of
wave-front.

Professor Maxwell, in 1853, sent to the Cambridge and Dublin
Mathematical Journal a problem about the path of a ray in
a medium in which

where /u0 and a are constant, and r is the distance from a fixed
point. Such rays, he points out, move in circles. This problem,
he mentions, was intended to illustrate the fact that the principal
focal length of the crystalline lens of the eye is very much shorter
than anatomists calculate it, from the curvature of its surface and
the index of refraction of its substance. The reason, he shows, is
the increase of density towards the centre of the lens, so that the

1863] CORRESPONDENCE WITH W. THOMSON AND P. G. TAIT 449

rays pass nearly tangentially through a place where the density is
varying. Also, in the Cambridge Examinations for 1870, Prof.
Maxwell set a question about the conditions of a horizontal ray of
light having a greater curvature than that of the earth. A great
deal, he says, has been written about atmospheric refraction by
Bessel, Clairaut, and others ; and a question has been set on it in
January of every year at Cambridge for several years back, so that
the subject has been much discussed in various ways; but, he
says, the mode of treatment of the subject in the present paper
does not seem to have been anticipated. — J. THOMSON.

[The following letters from JAMES to WILLIAM THOMSON, and
from Professor TAIT to JAMES THOMSON, relate to the fore-
going important paper and are of historical interest.]

6th November 1863.

DEAR WILLIAM,

The foregoing investigation wa3 worked out a few days
ago by Professor Purser (Prof, of Mathematics in Queen's College,
Belfast) when I proposed the question to him which forms the
heading of the investigation. As here written out it is stated at
much greater length or with fuller explanations than he gave it.
Perhaps he would think some of the steps needless, but this form
is that in which I have made it clear to my own mind.

From the result of the investigation : — namely, that the cur-
vature of the ray of light approaches to a maximum as the
inclination of the ray approaches to horizontality, I conclude that
a level ray directed so that, if it were to move straight forward, it
would pass along an infinitely thin lamina of uniform density but
with less density above and greater below, would be bent by the
influence of the difference of densities above and below it.

You are aware that I have for several years been turning
attention to the questions here discussed. It was an idea of mine
that writers on Engineering levelling were not entitled, from the
mere consideration of the refraction of a ray of light descending
obliquely through the atmosphere to run to the conclusion that
a level ray entering a levelling instrument would have any curva-
ture due to refraction, because it is really passing along a lamina

T. 29

450 MISCELLANEOUS PAPERS [63

of uniform density along the path of the ray of light, and not
passing obliquely from laminae of less to laminae of greater
density. I thought it probable that the radius of curvature
would be infinite for a level ray, as well as for a vertical ray ; and
that it would have a minimum value for some particular angle of
inclination of the ray.

When I mentioned the matter to you, you thought on a slight
consideration as I did, that a ray passing horizontally along a
lamina of uniform density along the path of the ray would not
be bent*.

Still the question appeared to me to be open for investigation,
that perhaps the refraction of a ray falling on a lamina at a very
small angle of inclination might be so great as to make the ray
have a finite curvature when infinitely nearly parallel to the
laminae. Prof. Tait tried to solve the question one evening;
observing the importance of the consideration last mentioned,
but he did not happen on any easy way of arriving at a solution,
and so he let the matter drop, I believe.

Professor Purser's solution as explained or developed more
fully in the foregoing is perfectly satisfactory to me. When I
pointed out to him the consequence I would draw from it : — that
a perfectly level ray would be refracted or bent into a curve of the
maximum curvature, he would not agree that such a conclusion
would be legitimate, as he said that as soon as the inclination of
the ray becomes Zero, the whole foundation and framework of the
investigation fails. Still I believe that my inference is perfectly
legitimate ; for I see that if his investigation proves a ray of light
to move along a certain curved path, when infinitely nearly level,
as also that the rate of change of curvature is Zero, as the in-
finitely small inclinations increase or diminish, it must follow that
a ray of light passing exactly level will be bent with the same
curvature as one infinitely nearly level ; as there is no sudden
change of any physical conditions that I can imagine at the
instant the ray becomes level from being infinitely nearly so.

I think Prof. Purser afterwards came to think that probably
my view on this matter is correct. What do you think of this ?
Of course it is to be recollected that the whole is founded on the
supposition (which we have no means at present of knowing to be

* [Note :— written August 1872. Dr Lloyd in his Optics, 1849, pages 108 and
109, seems deliberately to think so too.]

1870] CORKESPONDENCE WITH W. THOMSON AND P. G. TAIT 451

true) that the ordinary law of refraction; viz. that the sine of
angle of refraction is proportional to the sine of the angle of
incidence ; holds good for rays of light falling with infinitely small
inclinations on infinitely thin laminae of the atmosphere.

If this be true, is it not the case that the conclusion I have
deduced is a new principle in optics, namely that a ray of light
passing exactly along a lamina with denser matter to one side
than to the other will bend itself towards the side where the
denser matter is ?

I am, Your affte. brother,

JAMES THOMSON.

17 UNIVERSITY SQUARE, BELFAST.
ZZnd March, 1870.

MY DEAR WILLIAM,

Will you look over the enclosed paper about Atmo-
spheric Refraction of Inclined Rays, and the Path of a Level Ray?
You may recollect my showing to you the investigation made out
by Prof. Purser on that subject some years ago. The investigation
I now give is, I think, greatly preferable ; and, so far as I know,
is quite new. In fact I am not aware of any investigation on the
subject previous to the one which Prof. Purser made out, when
I put the matter before him as one of importance. If you care to
see the investigation made by Prof. Purser, I can send you a copy
of it as written out and explained by me at the time when it
was new.

The subject is of much practical importance in respect to
putting people concerned in extensive geodesical operations on
right modes of considering the possible or probable effects of the
atmosphere on long sights taken with the Levelling Instrument....

I am, Your affte. brother,

JAMES THOMSON.

17 DRUMMOND PLACE, EDINBURGH.
25*A April 1870.

MY DEAR THOMSON,

Your brother sent me the accompanying paper to
read. As I am alluded to in it, I would only say that I hope it
may be correct, because it gives us if true (by means of total
internal reflection) a hint of the nature of transparent bodies

29—2

452 MISCELLANEOUS PAPERS [64

very close to their surfaces; in fact it reproduces Poisson's as-
sumption in his theory of Capillary Forces.

But I see one very formidable objection — viz. that the direc-
tion of propagation of light is only normal to the wave front in
homogeneous singly refracting media. So that I see at present
no reason for believing that if the earth were plane and the
density of the air depended on the height only, a horizontal
beam should . not remain horizontal while its wave-front takes
all possible inclinations. I have been too busy of late to work
at the subject properly, and what I now write is the result of
conjecture merely. So it is quite likely that you may5 disprove
it*, — only it will be necessary to do so as, if what I hint is possible,
your demonstration breaks down.

Yours truly,

P. G. TAIT.

64. ON AN INTEGRATING MACHINE HAVING A NEW KINEMATIC

PRINCIPLE.

[From the Proceedings of the Royal Society, Vol. xxiv, 1876, p. 262. This
paper was followed in Proc. Eoy. Soc. by three short papers of the same
date by Sir William Thomson. The whole series of papers is reprinted
in Thomson and Talt, Natural Philosophy, Ed. 2, part i, 1879, pp. 488—
508 under the Titles: — 'An Instrument for calculating the Integral of
the Product of two given Functions ' ; ' Mechanical Integration of Linear
Differential Equations of the Second Order with Variable Coefficients ' ;
'Mechanical Integration of the general Linear Differential Equation of
any Order with Variable Coefficients.']

THE kinematic principle for integrating ydx, which is used
in the instruments well known as Morin's Dynamometerf and

* [Its truth is implied in the law of refraction of the rays, which here constitutes
their definition. The argument can moreover be conducted in terms of wave-
fronts alone, without mentioning rays.]

t Instruments of this kind, and any others for measuring mechanical work,
may better in future be called Ergometers than Dynamometers. The name
"dynamometer" has been and continues to be in common use for signifying a
spring instrument for measuring force ; but an instrument for measuring work,
being distinct in its nature and object, ought to have a different and more suitable
designation. The name " dynamometer," besides, appears to be badly formed from
the Greek ; and for designating an instrument for measurement of force I would
suggest that the name may with advantage be changed to dynamimeter. In respect
to the mode of forming words in such cases, reference may be made to Curtius's
Grammar, Dr Smith's English edition, § 354, p. 220.— J. T., 26th February, 1876.

1876] ON AN INTEGKATING MACHINE 453

Sang's Planimeter*, admirable as it is in many respects, involves
one element of imperfection which cannot but prevent our con-
templating it with full satisfaction. This imperfection consists in
the sliding action which the edge wheel or roller is required to
take in conjunction with its rolling action, which alone is desirable
for exact communication of motion from the disk or cone to the
edge roller.

The very ingenious, simple, and practically useful instrument
well known as Amsler's Polar Planimeter, although different
in its main features of principle and mode of action from the
instruments just referred to, ranks along with them in involving
the like imperfection of requiring to have a side wise sliding action
of its edge rolling wheel, besides the desirable rolling action on
the surface which imparts to it its revolving motion — a surface
which in this case is not a disk or cone, but is the surface of the
paper, or any other plane face, on which the map or other plane
diagram to be evaluated in area is drawn.

Professor J. Clerk Maxwell, having seen Sang's Planimeter in
the Great Exhibition of 1851, and having become convinced that
the combination of slipping and rolling was a drawback on the
perfection of the instrument, began to search for some arrange-
ment by which the motion should be that of perfect rolling in
every action of the instrument, corresponding to that of combined
slipping and rolling in previous instruments. He succeeded in
devising a new form of planirneter or integrating machine with
a quite new and very beautiful principle of kinematic action
depending on the mutual rolling of two equal spheres, each on
the other. He described this in a paper submitted to the Royal
Scottish Society of Arts in January 1855, which is published in
Vol. IV. of the Transactions of that Society. In that paper he also
offered a suggestion, which appears to be both interesting and
important, proposing the attainment of the desired conditions of
action by the mutual rolling of a cone and cylinder with their
axes at right angles.

The idea of using pure rolling instead of combined rolling and
slipping was communicated to me by Prof. Maxwell, when I had
the pleasure of learning from himself some particulars as to the

* Sang's Planimeter is very clearly described and figured in a paper by its
inventor, in the Transactions of the Royal Scottish Society of Arts, Vol. iv.
January 12, 1852.

454 MISCELLANEOUS PAPERS [64

nature of his contrivance. Afterwards (some time between the
years 1861 and 1864), while endeavouring to contrive means for
the attainment in meteorological observatories of certain integra-
tions in respect to the motions of the wind, and also in endeavour-
ing to devise a planimeter more satisfactory in principle than
either Sang's or Amsler's planimeter (even though, on grounds
of practical simplicity and convenience, unlikely to turn out
preferable to Amsler's in ordinary cases of taking areas from
maps or other diagrams, but something that I hoped might
possibly be attainable which, while having the merit of working
by pure rolling contact, might be simpler than the instrument of
Prof. Maxwell and preferable to it in mechanism), I succeeded in
devising for the desired object a new7 kinematic method, which
has ever since appeared to me likely sometime to prove valuable
when occasion for its employment might be found. Now, within
the last few days, this principle, on being suggested to my brother
as perhaps capable of being usefully employed towards the develop-
ment of tide-calculating machines which he had been devising, has
been found by him to be capable of being introduced and combined
in several ways to produce important results. On his advice,
therefore, I now offer to the Royal Society a brief description
of the new principle as devised by me.

The new principle consists primarily in the transmission of
motion from a disk or cone to a cylinder by the intervention of
a loose ball, which presses by its gravity on the disk and cylinder,
or on the cone and cylinder, as the case may be, the pressure
being sufficient to give the necessary frictional coherence at each
point of rolling contact ; and the axis of the disk or cone and that
of the cylinder being both held fixed in position by bearings in
stationary framework, and the arrangement of these axes being
such that when the disk or the cone and the cylinder are kept
steady, or, in other words, without rotation on their axes, the ball
can roll along them in contact with both, so that the point of
rolling contact between the ball and the cylinder shall traverse
a straight line on the cylindric surface parallel necessarily to the
axis of the cylinder — and so that, in the case of a disk being
used, the point of rolling contact of the ball with the disk shall
traverse a straight line passing through the centre of the disk —
or that, in case of a cone being used, the line of rolling contact of
the ball on the cone shall traverse a straight line on the conical

1876] ON AN INTEGRATING MACHINE 455

surface, directed necessarily towards the vertex of the cone. It
will thus readily be seen that, whether the cylinder and the disk
or cone be at rest or revolving on their axes, the two lines of
rolling contact of the ball, one on the cylindric surface and the
other on the disk or cone, when both considered as lines traced
out in space fixed relatively to the framing of the whole instrument,
will be two parallel straight lines, and that the line of motion of
the ball's centre will be straight and parallel to them. For
facilitating explanations, the motion of the centre of the ball along
its path parallel to the axis of the cylinder may be called the
ball's longitudinal motion.

Now for the integration of ydx : the distance of the point of
contact of the ball with the disk or cone from the centre of the
disk or vertex of the cone in the ball's longitudinal motion is to
represent y, while the angular space turned by the disk or cone
from any initial position represents x ; and then the angular space
turned by the cylinder will, when multiplied by a suitable constant
numerical coefficient, express the integral in terms of any required
unit for its evaluation.

The longitudinal motion may be imparted to the ball by
having the framing of the whole instrument so placed that the
lines of longitudinal motion of the two points of contact and of
the ball's centre, which are three straight lines mutually parallel,
shall be inclined to the horizontal sufficiently to make the ball
tend decidedly to descend along the line of its longitudinal motion,
and then regulating its motion by an abutting controller, which
may have at its point of contact, where it presses on the ball,
a plane face perpendicular to the line of the ball's motion. Other-
wise the longitudinal motion may, for some cases, preferably be
imparted to the ball by having the direction of that motion hori-
zontal, and having two controlling flat faces acting in close contact
without tightness at opposite extremities of the ball's diameter,
which at any moment is in the line of the ball's motion or is
parallel to the axis of the cylinder.

It is worthy of notice that, in the case of the disk, ball, and
cylinder integrator, no theoretical nor important practical fault in
the action of the instrument would be involved in any deficiency
of perfect exactitude in the practical accomplishment of the
desired condition that the line of motion of the ball's point of
contact with the disk should pass through the centre of the disk.

456

MISCELLANEOUS PAPERS

[64

The reason of this will be obvious enough on a little con-
sideration.

The plane of the disk may suitably be placed inclined to the
horizontal at some such angle as 45° ; and the accompanying
sketch, together with the model, which will be submitted to the
Society by my brother, will aid towards the clear understanding
of the explanations which have been given.

My brother has pointed out to me that an additional operation,
important for some purposes, may be effected by arranging that
the machine shall give a continuous record of the growth of the
integral by introducing additional mechanisms suitable* for con-
tinually describing a curve such that for each point of it the
abscissa shall represent the value of x, and the ordinate shall

D, the Disk.

A, the Axle of the Disk.
C, the Cylinder.

E E, the Axle or the Journals of
the Cylinder.

B, the Ball.

PLAN

represent the integral attained from # = 0 forward to that value
of x. This, he has pointed out, may be effected in practice by
having a cylinder axised on the axis of the disk, a roll of paper
covering this cylinder's surface, and a straight bar situated
parallel to this cylinder's axis and resting with enough of pressure
on the surface of the primary registering or the indicating cylinder
(the one, namely, which is actuated by its contact with the ball)
to make it have sufficient frictional coherence with that surface,

1876] ON AN INTEGRATING MACHINE 457

and by having this bar made to carry a pencil or other tracing
point which will mark the desired curve on the secondary register-
ing or the recording cylinder. As, from the nature of the apparatus,
the axis of the disk and of the secondary registering or the recording
cylinder ought to be steeply inclined to the horizontal, and as,
therefore, this bar, carrying the pencil, would have the line of its
length, and of its motion alike steeply inclined with that axis, it
seems that, to carry out this idea, it may be advisable to have
a thread attached to the bar and extending off in the line of the
bar to a pulley, passing over the pulley, and having suspended
at its other end a weight which will be just sufficient to counteract
the tendency of the rod, in virtue of gravity, to glide down along
the line of its own slope, so as to leave it perfectly free to be
moved up or down by the frictional coherence between itself and
the moving surface of the indicating cylinder worked directly by
the ball.

The following correspondence with Prof. Clerk Maxwell ensued.

GLENLAIR, DALBEATTIE,
26th June, 1879.

DEAR PROFESSOR THOMSON,

In the description of the disk globe and cylinder
integrator as given in the new edition of T and T', the position
of the globe is determined by means of a fork with two flat faces,
which graze the opposite sides of the sphere without nipping it,
or else by one flat face and gravity.

Now it is easy to ensure that the friction of these surfaces on
the sphere shall be small in comparison with that at the contacts
with the disk and cylinder, but it occurs to me that the motion of
the surface of the globe at the points of contact of the fork relative
to its centre is perpendicular to the plane containing the two lines
of contact of the sphere with the disk and cylinder. Hence if
instead of a flat face we place a cylinder having its axis perpen-
dicular to the lines of contact and in a plane through the centre
of the sphere parallel to the plane through the lines of contact,
and if this cylinder is free to rotate about this axis, there will be
rolling without slipping between this (guiding) cylinder and
the sphere.

458 MISCELLANEOUS PAPERS [64

It is evident that when the sphere is changing its " position "
by rolling on the disk and cylinder, these being at rest, there will
be pure rolling between the sphere and guiding cylinder. When
the disk moves, the position of the globe being fixed, the globe
spins upon the point of contact with the guiding cylinder.

Hence for all motions of the machine the action between the
globe and guiding cylinder (or cylinders if there is another on
the other side) is pure rolling.

Yours very truly,

J. CLERK MAXWELL.

OAKFIELD HOUSE, UNIVERSITY AVENUE,
GLASGOW, 16 July 1879.

MY DEAR PROFESSOR MAXWELL,

I duly received your letter of the 25th of June, and
was much interested by your device of the cylindric roller, for
giving a perfect rolling contact at the one or two guide or guides
or terminals of guide fork for the ball in the integrator.

What you propose is very nice indeed as a kinematic con-
trivance, or as a means for accomplishing a condition that might
possibly in some way be wanted. The instrument as already
devised with sliding contact at the guide face or faces, is not
subject, I would say, and I think you mean also, to any practical
or theoretical objection from the sliding contact, at the point of
contact of the globe with the guide, because all we want is to
have hesion at the points of contact of the globe with the cylinder
and disk, and this is not at all hindered by the frictional sliding
motion at the face of contact of the guide with the ball. I suppose
we are entitled to say that this frictional resistance at the guide is
not a theoretical objection nor a practical objection, unless also we
were to treat the frictional resistance of the journals or axle of the
cylinder (which receives its motion through the ball) as objection-
able. Of course if the point of contact of the ball with the disk
and cylinder be considered (in virtue of yielding of the materials)
as not being quite mathematical points, we may see that there
would be an almost innnitesimally small theoretical imperfection
introduced by anything requiring the transmission of mechanical
energy from the disk through the globe to the cylinder, or indeed
the transmission of energy either way between the disk and globe

1879] CORRESPONDENCE WITH J. CLERK MAXWELL 459

or between globe and cylinder : and in this sense any expenditure
of energy in friction at the guide of the globe would be an almost
infinitesimally small theoretical fault. This, however, I think
may be left out of account, as being small relative to the ordinary
inaccuracies incidental to all kinds of instruments.

Your guide cylindric roller, though nice for geometrical or
kinematic consideration, would I think increase the difficulty and
cost of construction of the machine, and would introduce new
liabilities to slight defects owing to imperfections of construction,
in ways from which the plane guide face contact with the ball
is quite free.

We are all well. If there is any chance of your being in this
region of Scotland this summer, I hope you will recollect that we
would be very glad to have a visit from you for as long as you
could stay. We are expecting to be at home most of this summer.

Mrs Thomson unites in kind regards,

Yours very truly,

JAMES THOMSON.

65. ON CERTAIN APPEARANCES OF BEAMS OF LIGHT, SEEN AS
IF EMANATING FROM CANDLE OR LAMP FLAMES.

[Posthumous paper, from the Proceedings of the Royal Society r, Vol. LII, 1892,
p. 70, communicated by LORD KELVIN, P.E.S., with an Introductory
Note.]

ABOUT the end of last January, when my brother was fully
occupied in writing his paper on the Trade Winds for the Bakerian
Lecture, he called my attention to the well-known beams or ladders
of light seen below or above a lamp flame viewed with partially-
closed eyelids, and he gave me verbally an explanation of the
phenomenon which surprised me very much. By some simple
and interesting trials with my own eyes, which he explained to me
how to make, I was perfectly convinced that his explanation was
correct ; and believing it, as I still believe it, to be new, I urged
him to write a short paper on the subject for the Royal Society,
but not to let it interfere with his work for the Bakerian Lecture ;
and he undertook to do so as soon as might be after being freed

460 MISCELLANEOUS PAPERS [65

from this work. We hoped, somewhat confidently, that he might
be able to give the thus promised paper before the end of the
present session of the Royal Society. That hope has not been
fulfilled, and I had offered to the Secretaries a communication
describing my recollection of what my brother had told me, when
his son found a memorandum of date 18th October, 1891, and
a little book of notes of date 29th December, which tell the story
better than I could have told it, and which, therefore, though not
completed in proper form for publication, I now give in the
unfinished form in which they have been found, with only a some-
what more clear drawing, and description of drawing, substituted
for the rough sketch found in his note of date October 18, 1891.

Proposed probable Paper for the (?) Society, by J. T., " On the
Nature and Origin of certain Appearances of Beams of Light
as if emanating from Candle or Lamp Flames!'

Description of the Drawing.

[The drawing represents a vertical section of the eye, eyelids,
and watery prismoids*, through FF', the axis of the eye. The
large number of parallel lines outside represent rays of light
coming from a flame several feet or yards away in the direction
of F't to the eyelids, the prismoids, and the undisturbed outer
surface of the cornea between the prismoids. The lines within
the eye below FF' represent the convergence to F, the image of
the fiame, of those of the external rays from the flame which fall
on the undisturbed portion of the surface of the cornea. The lines
within the eye above FF' represent rays disturbed by the prismoid
of the upper eyelid which, incident on the retina at bbb, give the
perception as if of light coming from without in the direction of
the dotted lines outside the eye. It is this perception that
constitutes the appearance of the downward beams or ladders of
light, due to the prismoid of the upper eyelid. The rays disturbed
by the prismoid of the lower eyelid, in the position represented in
the diagram, are all stopped by the lower part of the iris.

Looking now at the diagram, we understand perfectly that
if, with the eyeball and flame unchanged, the upper eyelid be
gradually raised a little, the uppermost of the rays coming inwards

* The refracting watery liquid in the entrant corner between lip of eyelid and
cornea may be called the prismoid or liquid prismoid.

1892] ON CERTAIN APPEARANCES OF BEAMS OF LIGHT 461

from the prismoid will fall on the upper part of the iris and will
be stopped by this screen. Thus, the length of bbb upwards from
F is diminished, until all the beams from the prismoid are stopped
by the iris, and the length of the apparent beams below the flame
correspondingly diminishes to zero. When the upper eyelid is
wide open the flame is seen without any appearance of the beams
below it. We also understand readily from the diagram how, if
the lower eyelid is lifted a little without any change in the
position of the upper eyelid, beams both above and below the

flame are seen. We also conclude that if, with the eyelids fixed
relatively to the head, the head is moved while the eyeball remains
with its axis in the direction of the flame, we see beams of light
above the flame when the head is turned upwards, and beams of
light below the flame when the head is turned downwards. Also
that if the eyelids are partially closed, as in the diagram, beams
will be seen both above and below the flame when the head,
carrying the eyelids with it, is turned slightly up from the position
shown in the diagram. Also that if the eyelids be wide open,
instead of half closed as shown in the diagram, no beams, either
above or below the flame, will be seen when the two eyelids are
equidistant, or nearly equidistant, above and below the middle of
the pupil. When the head, with the eyelids, is turned downwards,
so as to bring the upper eyelid across the aperture of the pupil
beams of light are seen below the flame ; and when the head, with
the eyelids, is turned upwards so as to bring the lower eyelid across
the middle of the pupil, beams of light produced by the prismoid
of the lower eyelid are seen above the flame.]

462 MISCELLANEOUS PAPERS [65

Notes on Quasi-Ray Beams of Light from Candles, or
other small Luminous Spots.

Date of Note, 29th December, 1891.

I have noticed decidedly this morning to the following effect : —

In some cases (the nature of which I intend to note further
on) I found that, when seeing a small gas flame with apparent
descending tail (or quasi-beam of rays), I could, by lowering the
upper eyelid, cut off vision of the flame, while leaving the tail
visible; and, by still further lowering the upper eyelid,* I could
cut off the upper part of the tail, leaving the lower part, the part
remote from the flame, quite visible as before. The contrast
between lowering the upper eyelid and lowering a screen (a card,
for instance) in front of the eye was very remarkable. In the
lowering of the card or other screen, the tail vanishes before the
flame is eclipsed; but in lowering the eyelid the flame is
eclipsed first.

In some attitudes I could not bring out these phenomena.
I did find them when awake in bed early in the morning, head
on pillow and light corning down from a gas flame obliquely to
the eye. Point to which eye was directed seemed to do best when
taken at an altitude (angular) somewhat above the gas flame.

Afterwards, this same morning, I found I could see the pheno-
menon when standing upright and looking at image of gas in
mirror. Ray from image ascending obliquely; eyesight directed
above image in looking-glass.

Again, looking at a gas flame a little above the level of the
eye, I stood erect and elevated my face, directing my eyesight
to above the gas; then lowered the upper eyelid and saw the
downward tail remaining when the gas flame was eclipsed by the
eyelid. The theory of all this is clear to me, and in agreement
with what I have previously devised. — J. T.

Take notice that to get the phenomena above sketched out
to show themselves, the edge of upper eyelid, where roots of
eyelashes are situated, must not shadow the prismoid when the
eyelid is lowered enough to cover the pupil from the direct rays
of the candle or gas flame. After the candle is cut off from the
pupil, the direct rays from the flame must still be reaching the
prismoid. This, I think, tallies with the experimental conditions

1892] ON CERTAIN APPEARANCES OF BEAMS OF LIGHT 463

under which the tail was seen when the flame was eclipsed by
eyelid.— J. T.

p.S. — Same day, 29th December. On a little further con-
sideration I notice that the elevation of the face is of no im-
portance. It is only the elevation of the line of special direction
of the eyesight [axis of the eye] relatively to the line from flame
to eye that is important. — J. T.

Notes on Quasi-Light Beams.
(For paper.)

Often I fail to see the apparently ascending beam above the
candle or gas flame. But I find that by very nearly shutting the
eye I can see the ascending beam going up very high and
the descending one at same time. On bringing my open hand
down from above as if to cut off the ascending beam I see the
beam as if between my eye and my hand, and the flame begins to
be eclipsed before the beam is cut off, or even diminished.

Note by the President of date June 16.

I had asked many friends well acquainted with optical subjects
whether they knew of this explanation of the luminous beams, and
all said " no " until yesterday evening, at the soiree of the Royal
Society, when Professor Silvanus Thompson immediately answered
by giving the explanation himself, and telling me that he had
given it to his pupils in his lectures on optics, as an illustration of
a concave cylindrical lens. He did not know of the explanation
ever having been published otherwise than in his lectures. I have
myself also looked in many standard books on optics, and could
find no trace of intelligence on the subject. It seems quite
probable, therefore, that, of all the millions of millions of men
that have seen the phenomenon, none, within our three thousand
years of scientific history, had ever thought of the true explanation
except Professor Silvanus Thompson and my brother*.

* [Cf. Life of Lord Kelvin, by Silvanus P. Thompson, vol. n. p. 919, footnote.]

APPENDIX

*

66. ON PUBLIC PARKS IN CONNEXION WITH LAKGE TOWNS,
WITH A SUGGESTION FOR THE FORMATION OF A PARK IN
BELFAST*.

[A Paper read before the Belfast Social Inquiry Society on the
2nd March, 1852.]

THE importance of public parks and other open spaces in large
towns is such as scarcely to admit of debate, yet the consideration
of some of the advantages resulting from them cannot fail to be
a matter of interest. They have a great effect in improving the
atmosphere of the districts around them, by allowing of the change
of air so much needed where many human habitations are closely
packed together. Thus the beneficial influence of the parks of
London extends to multitudes even of those who seldom use them
as places for recreation and exercise. When, however, one leaves
the hot and crowded streets of London on a summer day, and,
entering one of the parks, passes along pleasant walks among
flowering shrubs, green grass, and ornamental patches of water
enlivened with numerous water-fowls of various kinds and colours,
he feels practically some of the advantages of open spaces in large
towns. When one walks in the Glasgow Green, as being the best
place for exercise within the town, or the best outlet from it to
the country, and when he sees himself surrounded on all sides
with tall chimneys vomiting smoke which is wafted past him in
clouds, although he may not feel disposed to congratulate himself
on the freshness of the air, yet still his reason convinces him that
the state of the town, bad as it is, would be much worse were this

* [This paper led directly to the purchase, for the town of Belfast, of the large
Ormeau Park.]

1852] ON PUBLIC PARKS IN CONNEXION WITH LARGE TOWNS 465

extensive space covered densely with mills and other buildings like
those with which it is surrounded. When the continental tourist
visits on a fine summer evening the promenades which surround
the city of Frankfort-on-the-Main, and enjoys the balmy freshness
of the air and the perfume of the flowers, while he watches with
pleasure the fire-flies as they float before him in the dusk, he is
forcibly struck with the contrast between the present condition
of the place, and its former state, when it was allocated for the
fortifications of the city. He rejoices that the modern system
of warfare has rendered all such fortifications unavailable, and
admires the good taste which has turned to such a useful and
agreeable purpose the space thus left vacant. Of all the thorough-
fares of Paris, the Boulevards are among the most agreeable, on
account of their spaciousness. These are also due to ancient
fortifications, which surrounded the city when it was much less
extensive than at present. Now, it is well worthy of remark, that
the original conservation of most of the open spaces at present
existing in towns has been due rather to accidental circumstances
than to a wise foresight in the allocation of the land and the
arrangement of the buildings. The open spaces in Frankfort and
Paris, to which I have just alluded, are examples of this fact.
Most of the parks of London, too, were originally the private
property of the Crown ; and, besides, they were formerly not open
spaces preserved in the city, but they were far away from it in
the country. It is only in later times that the town has spread
itself round them so as to include them within its precincts. The
name of the church at Charing Cross, St Martin's-in-the-Fields,
affords a striking indication that at the time when it was built
it was outside of the metropolis ; and yet, the whole line of
parks, comprising St James's Park, Green Park, Hyde Park, and
Kensington Gardens, lies still farther away from the original city.
The Dublin College Park was not, at the time of the foundation of
the University, within the town. The charter of Queen Elizabeth,
establishing the college, designates it as the College of the Holy
Trinity, near Dublin. The Glasgow College Green, also, was
originally outside of the town ; and, even at the present day,
the college, though surrounded by the town, is still a separate
corporation, not being subject to the municipal authorities.

Although, then, in former times very little foresight was
applied in the disposition of the buildings and open spaces of

T. 30

466 APPENDIX [66

increasing towns, yet in our own times better methods have been
commenced. Great good has already resulted from the labours
of the Health of Towns' Commissioners, and I may be allowed to
read their report and recommendation, respecting public parks
and open spaces, given about seven years ago ; especially as con-
siderable improvements have been effected, since that time, in
some of the places referred to in the report.

" In the course of our inquiries into the sanatory state of large
towns and populous districts, where a high rate of mortality and
much disease is prevalent, we have noticed the general want of
any public walks, which might enable the middle artd poorer
classes to have the advantage of fresh air and exercise in their
occasional hours of leisure. With regard to all open spaces,
especially well ordered squares, ornamented by trees or gardens,
which already exist in the metropolis and large towns, we strongly
recommend their preservation from any encroachment by public
or private buildings. Although not open to the public, they con-
tribute largely to the general salubrity of a town ; and it has too
commonly happened that, as population has increased, almost every
open space has been enclosed ; thus, at the same time, excluding
the people from their former places of exercise and recreation,
and preventing that ventilation which would otherwise have been
preserved.

" We have found this state of things very generally lamented
by the inhabitants of large towns, and a very prevalent desire
existing in many of them, and shared by benevolent persons of
the more opulent classes elsewhere, to repair this deficiency.

"The great towns of Liverpool, Manchester, Birmingham,
Leeds, and very many others, have at present no public walks.
Shrewsbury, Newcastle-under-Lyme, Derby, and a few more,
possess them.

"The metropolis, except at the west and north-west, where
the different parks minister so much to the comfort and health
of the people, has no public walks, though the Victoria Park, now
in progress, will supply this want towards the east.

"The large population of Southwark and Lambeth, to the
south of the Thames, are yet without such a source of enjoyment
and salubrity.

"This subject was considered by a Select Committee of the
House of Commons in 1833, who strongly recommended steps

1852] ON PUBLIC PARKS IN CONNEXION WITH LARGE TOWNS 467

should be taken to supply the want. In 1840 the sum of £10,000
was voted by Parliament, to assist local efforts for this purpose in
provincial towns ; and a few places have had grants from that sum
for this purpose.

" In any attempt to carry out these objects, we do not anti-
cipate so much difficulty as has by many been apprehended. It
sometimes happens that there is a common, or waste lands, in the
vicinity, which, by an alteration of the law, and proper compensation
given, might be made available for this purpose. The formation
of a public walk would, in such case, at the same time minister
to the comfort and improve the health of the inhabitants by a
proper drainage of the lands in their vicinity. In many cases
local exertion and munificence would accomplish the object, if
some moderate assistance were given.

"We therefore recommend that, for the purpose of aiding the
establishment of public walks, in addition to the legal facilities
adverted to, the local administrative body be empowered to raise
the necessary funds for the management and care of the walks
when established!'

Manchester, I am glad to say, has now three public parks,
though at the time of the report it had none. Victoria Park, in
the east of London, is also now opened, and it confers a great
benefit on that locality. The case of Manchester may serve as
a very important lesson to other towns of smaller size. While,
on the one hand, its three parks, obtained in so short a time, may
afford great encouragement, on the other, their situation, so far
distant from the centre of the town, ought to be taken as a very
serious warning. The town was allowed to extend itself uninter-
ruptedly outwards from a centre, no open space being preserved ;
and then, when parks came to be imperatively demanded, sites
for them were not to be obtained except in the suburbs ; and the
central parts of the town are but little benefited. Thus, although
their formation constitutes a tardy acknowledgment of past error,
it provides no adequate remedy for the evil consequences.

With the manufacturing system, which has sprung up so
wonderfully in the last fifty or sixty years, and which has caused
the rapid extension of so many towns, there has also arisen a
greatly increased want of space for ventilation of the towns, and
for healthful recreation of the inhabitants. While, on the one
hand, it has greatly augmented the wealth of many classes of

30—2

468 APPENDIX [66

society, and has supplied the wants of almost all more abundantly
than would otherwise have been possible; it has still, on the
other hand, entailed on the inhabitants some discomforts or in-
conveniences to which they were formerly not subject. Of these,
the principal are, smoky air, and an increased distance of their
residences from the country. Why then, I would ask, when
manufactures have done so very much to increase riches, why
should the possessors object to spend some small part of those
riches in obviating the concomitant evils of the manufacturing
system ? They do already frequently spend large sums for the
sake of enabling themselves and their families to escape from
town for greater or less portions of their time. Many of them,
however, still find themselves obliged to live entirely in town, or,
at least, to spend the greater part of their time in it. Would it
not, then, be well that they should do their best to render town
a pleasant place of residence ? To effect this desirable object,
the establishment of public parks is certainly one of the most
important steps.

Now, where does the difficulty lie ? It must be attributed,
in a great degree, to the fact that the want of a park in any
particular locality is but little felt at the time when the land
can be easily procured, and that, when the want is felt, the
space, being already covered with valuable property, cannot be
obtained unless at a cost which practically amounts to a pro-
hibition. Persons residing at the outskirts of an increasing town
can commonly make their way to the country when they want
exercise, and in their houses they get a tolerable share of air
fresh from the country. The individual proprietors of land at
the outskirts wish to make the most of their property, and so
they usually build closely, or, at most, leave vacant only such
small patches of gardens and shrubberies as will remunerate them
by increasing the value of their adjacent houses. The building
operations commonly proceed without any consideration for the
previously existing interests of the owners of property in the in-
terior of the town, which, in respect to suitableness for dwellings,
is deteriorated the farther it becomes swallowed up among dense
masses of houses. Of so much importance does this matter appear
to me, that I have long been of opinion, that we ought to have a
legislative enactment, laying a moderate tax on all land adjoining
a town as soon as, in virtue of the increase of the town, it comes,

1852] ON PUBLIC PARKS IN CONNEXION WITH LARGE TOWNS 469

for the first time, to be built on. The object of the tax would be
to supply funds for the establishment of permanent open spaces
wherever they would be judged most suitable, as a compensation
in kind for the sanatory evil to which I have referred, as being
inflicted on the interior of the town by buildings erected at the
outskirts. Even the proprietors round the outskirts, as a body,
need not complain of the system of taxation which I have pro-
posed. Their land is constantly receiving accessions of value as
the town spreads ; and this is not in consequence of any exertions
of their own, but rather of the industry and energy of the people
already established in the town. Besides this, they should re-
collect that, for every portion of land preserved open, nearer than
theirs to the town, the buildings will advance outwards the more
quickly, communicating to the land an increased value by their
approach.

Although I would advocate the propriety of a legislative
enactment such as I have briefly described, yet, as long as it
is wanting, I consider that we should by no means stand idly
waiting for it, but that we should adopt the best modes of pro-
cedure within our power for the accomplishment of our ultimate
object. Let us not exemplify the fable of "Rusticus expectat dum
transeat amnis " — (The clown stands waiting for the river to flow
past). The recommendation of the Health of Towns' Commis-
sioners, which I have already quoted, contains what, in the present
state of the law, appears to me to be the best mode of procedure
available — that, namely, of private subscriptions, aided by public
grants.

Having said thus much on remedial measures for the smoky
atmosphere of towns, I may be excused in adding here a few
statements in regard to preventive measures against the smoke
itself.

Numberless have been the schemes proposed and tried for
procuring a perfect combustion of coals in furnaces. These, how-
ever, have, in general, proved so unsatisfactory as to create the
idea that any farther attempts are likely to be fruitless; and
that the only thing to be done is to let the fireman bring about
the combustion as best he can, by carefulness and regularity in
supplying coals to the furnaces. There is no doubt that much
can be effected by skill and care on the part of the fireman ; but
still it is exacting too much from him to demand that he must

470 APPENDIX [66

send out no dense black smoke from the chimney. Using very
good coals, and having a furnace large in comparison to the
quantity of coals consumed, he may succeed tolerably well in
avoiding smoke; but, in ordinary cases, he will be unable to
attain anything like a perfect combustion. Whatever impression
may be made on people's minds by the numerous failures which
have occurred, the application of correct scientific principles to
this subject has, as is usually the case, led to the most favourable
results. One smoke-consuming furnace, at least, has for several
years been in successful operation ; not only avoiding the genera-
tion of smoke, but also, as I am convinced, economising Both fuel
and labour. I refer to Juckes' patent self-feeding furnace. The
perfect combustion is effected simply by a more regular process of
firing than is possible on the part of an attendant, this regularity
being combined with the principle of making the coals burn from
their upper surface downwards, no black coals being thrown on
the top of red-hot ones, and so no air passing from the red coals
through the black.

I come now to the part of my subject in which I feel by far the
deepest interest — the proposal for the formation of a public park
in the town of Belfast. The present condition of this town, and
its prospects for the future, seem to me to render the establish-
ment of open spaces highly desirable; and I consider that, just at
the present time, the town possesses, for such an undertaking, one
of those golden opportunities which are seldom met with, and
which, if allowed to pass, must be lost for ever.

During the progress of the town, an extensive space of ground,
situated between the Linen Hall and Donegall Pass, has, through
the pestiferous influence of a most intolerable nuisance, been kept
nearly free from buildings. The best dwelling-houses have been
effectually repelled from it by the dam on the Blackstaff, and as
yet only a few buildings have been erected in its vicinity, while
the town has sent out a branch on each side, and is now spreading
itself out beyond in the neighbourhood of the Botanic Garden
and the Queen's College. On the nearly vacant space under
consideration manufacturing establishments have already begun
to rise, and it is clear that, if this process be not stayed in time,
the best parts of the town for the transaction of business will
become almost completely hemmed in with mills and second or
third rate houses, all good approaches from the country being

1852] ON PUBLIC PARKS IN CONNEXION WITH LARGE TOWNS 471

cut off. The people of Belfast have thus the future destiny of
the town placed in their hands. They cannot help fixing, within
a very short period, whether the town is to become a densely
built and smoky place, good enough, indeed, for the prosecution
of work, but not fit for the enjoyment of life, or whether it is to
possess a public ornament which will be a source of admiration
in all time to come. One very desirable requisite for a park is
possessed by the ground in question. It has on it at present a
considerable number of trees already well grown. The importance
of this may be judged from the high value set by the people of
London on their trees. We all know that rather than condemn
a row of lofty elms to the axe, to make room for the Exhibition
Building, they preferred to carry a spacious arch of glass over the
summits of the trees. With reference to this subject, too, it may
be well to recollect that one of the most attractive and most
admired features of the Belfast Botanic Garden is due to the
selection, at the time of its formation, of a piece of ground on
which trees were already growing. While pleading for the con-
version of the effects due to the baneful influence of the Blackstaff
into a source of increase to the amenities of the town of Belfast,
I may direct attention to one case in which a permanent benefit
has been derived by this town from the former existence of a
nuisance. The wideness of High Street was determined by the
presence of a dirty stream which formerly flowed uncovered down
the middle of the street. Let us hope that the evils of the Black-
staff may be turned to good in a tenfold degree.

With reference to the extent of the proposed park, I wish here
to state that I would not confine my views to the space between
the Linen Hall and Donegall Pass. There lies a most tempting
piece of additional land between Donegall Pass and the Lagan,
in the direction towards Ormeau Bridge and the Queen's College.
The exterior limits of the park may, however, be safely left for
future consideration*.

The subject I have now brought before you shows the necessity
of attending early to projected public improvements, which can be
effected only by the combined action of many persons, and which
are of such a kind that the advantages to result from them, if

* At the meeting of the Society, in a discussion which followed the reading of
the present paper, several other desirable sites for parks were mentioned by various
members.

472 APPENDIX [67

carried out, would be shared in various degrees by multitudes
of individuals, as much by those who would give no aid in the
undertaking as by those who would make the greatest sacrifices,
whether of their time or of their money. It may be, that the
entire cost would prove almost inappreciable if compared with
the benefits which would accrue ; and yet, from the difficulty of
apportioning the burden of the undertaking among those who are
able and who ought to bear it, the improvement too often remains
neglected till the time for effecting it is past, and it has become
no longer possible. When this has been the case, regret for the
past is vain, unless it impel us to employ more foresight,* and to
apply more vigorous exertions for the future.

All inquiries into the advantages of such improvements, into
the difficulties and impediments which obstruct their introduction,
and into the best means of removing these, are essentially social
questions, and fall peculiarly within the province of a Social Inquiry
Society. The discussion of such questions, I may be permitted to
say, is not to be looked on as a mere barren debate. The ultimate
purpose is a practical one ; and when persons meet together in a
true spirit of candid inquiry, and with a genuine wish to promote
good objects, their efforts are sure to be, in many cases, crowned
with success.

67. NATIONALIZATION OF PUBLIC WORKS.

[From The Northern Whig of January 21, 1869.]

THE annual meeting of the Belfast Engineering and Archi-
tectural Association was held in the Athenaeum on Friday evening,
the 15th January, 1869— Professor James Thomson, M.A., C.E.,
presiding. The meeting being opened, the minutes were read
by the secretary, Mr Kelly ; after which Professor Thomson, who
had been elected as President for the year 1869, delivered his
opening address.

He stated that he had selected, as the subject to which he
would limit his address, a question which is of great and wide-
extending interest in connexion with engineering works through-
out the world, and which at present is one of special importance

1869] NATIONALIZATION OF PUBLIC WORKS 473

in reference to engineering affairs in Ireland. It was the question
of the advisability of nations or communities, instead of companies,
being the owners and governors of such works for public use, as,
from their nature, must be more or less of the nature of monopolies,
and do not admit of efficient competition ; and, in particular, the
question now rapidly advancing in public consideration, of the pur-
chase by the State of the Irish railways ; so that the people of
Ireland would virtually become the owners of the railways in their
own country. In general, he was in favour of the principle of
having all such works owned and governed by the nations or
communities for whose use they exist. Railways, extending
throughout an entire country, and being for the use of the
public generally, should belong to the State ; while town water
works and gas works, with their respective pipes under the
public streets, ought properly to belong to the local community
for whose special use they are established. He could not main-
tain, however, that local government arrangements in Ireland are
as yet sufficiently perfect to render our towns in general quite
ripe for organising and managing advantageously, on their own
behalf, without the intervention of companies, such undertakings
as the gas manufacture. He referred to a paper by John Han-
cock, Esq., J.P., published in the Transactions of the Social Science
Association for its recent meeting at Belfast, as giving a valuable
exposition of the local government question in its application to
Ireland, and pointed to indications of a growing determination
to have local government arrangements made much more perfect
than hitherto, and kept so. He expressed his confidence in the
safety of trusting every local monopoly to local government pro-
perly organised and checked. He proceeded to point out that
the working of railways by companies does not accord with the
general interests of the public. The aim of companies must
naturally be to bring about the maximum of profit to them-
selves, with the minimum of trouble and risk. Their tendency
will be to accommodate their arrangements to the convenience
of the public, and their fares and charges for passenger and
goods traffic to its advantage, just so far as, and no farther
than, in their opinion will conduce to good dividends to them-
selves on their shares. A Board of Directors of a railway, who,
by raising the fares and other charges, could show that they
brought about an increased dividend, though accompanied by a

474 APPENDIX [67

diminution of traffic, would be deemed to have performed good
service to their company; but this change would have effected
a pecuniary loss to every one of the public who travelled on the
railway, or sent goods by it, and would have prevented others
from getting the benefit of using the railway in many cases,
in which, under some other financial arrangements, they might
have used it, and might have contributed something towards its
expenses. The benefit conferred on the public, in respect to
passenger traffic — if we take for brevity the case of passenger
traffic alone — is far above the total of the fares. Because the
traveller is himself the best judge of the probable value !o him
of his intended journey. He will not undertake the journey unless
he believes it to be worth to him at least as much as the fare ;
and so we may consider the fare as indicating the value of any
such journey as is just at the point of being indifferent as to
whether it be worth undertaking or not ; but then it is inevitable
that scarcely any can be just at that exact point. Any contem-
plated journey below it will not be undertaken ; and nearly all
journeys made will be above it. Many a time a person goes a
journey by rail which he would value at five, ten, or twenty times
the amount of the fare; often at one and a half, two, or three
times. That relates only to actual travellers on the rail who
really pay fares, and so contribute towards the reimbursement
of the first costs and working expenses of the undertaking. But
also those who happen not to require to travel on a certain rail-
way near them, do receive a highly beneficial power or right,
which must have to them a real value — the power, namely, of
travelling by that railway whenever circumstances may lead them
to want to go. It may properly be esteemed by any member of
the community as a matter of importance and of value to him to
have a railway kept constantly in readiness for him if wanted
to carry him rapidly and easily over what otherwise would be
a long, fatiguing, and perhaps costly journey. Yet he has con-
tributed nothing towards its construction in consideration of the
advantage he holds in virtue of its existence. Thus, on the prin-
ciple of having a country's railway made and worked by companies,
the people benefited by the formation and maintenance of each
railway are not all duly brought in as contributors. Those who
do travel must then be charged for each journey, if the railway
is to be successful to the shareholders, more than would be re-

1869] NATIONALIZATION OF PUBLIC WORKS 475

quired if the contributions were levied for the railway from a
larger portion of the public benefited. A conclusion thence is,
that it is sound policy, in the interest of the general public, not
to arrange for levying the whole of the funds for payment of
interest or profit on the original outlay, and of working expenses,
by fares ; but inasmuch as the general public hold a benefit in
having the railway kept ready for them, whether they happen
to have occasion to use it or not, they should pay by taxation,
and especially by local taxation levied on the districts specially
benefited, something towards the attainment of that benefit ; and
then that every person in travelling should have lower fares to
pay, and have his interest and convenience generally better pro-
vided for, than under the present arrangements of the railways as
owned and worked by companies. Another conclusion is that the
construction of a railway is not to be considered as on the whole
a disastrous misapplication of labour and capital, even if the in-
come for the promoters, raised by charges on passenger and goods
traffic, be totally inadequate to pay fair interest on the money
sunk in their shares. In many such cases it is quite possible
that the only matter to be regretted may be that some other
method more in unison with sound policy for the general interests
of the public had not been contrived and adopted for levying the
funds for the expenses of the undertaking. The policy thus ad-
vocated, though it would be a great change from what we are
accustomed to in railway affairs, would really be no innovation
with reference to well-established and successful modes of con-
ducting other undertakings for public use. Common roads in
Ireland are already exempt from tolls, and are paid for by taxation.
The person using them for a journey, or for conveyance of goods,
has not anything to pay, even for the wear or injury of the road
due to his using it. This freedom to use the road goes far beyond
what in any case would be proposed in railways, because in them,
according to any propositions that are likely seriously to be put
forward, local taxation would only be looked for to supply a fund
supplemental to an important income to be derived from passenger
fares and charges on goods traffic. He pointed to other cases of
very different kinds of public undertakings admitted to be of high
public value, in which the idea of having the necessary funds levied
directly as charges on the use of what is made available would be
altogether untenable. One of these was that of the Ordnance

476 APPENDIX [67

Survey — an undertaking of great and general public value, and
yet impossible to be done at all, if allowed only on the condition
that the price of the maps sold must be fixed at such a rate as
that the costs of the survey shall be compensated for by the
income from the sale of the maps. Whether the price be fixed
at a high rate per map, or at a low rate per map, the cost of the
survey could not be compensated for in that way; and yet no
one will say that surveys of countries should for that reason be
necessarily deemed misapplications of money, skill, and work.
Bridges repeatedly have been built at great cost, and for long
years, owing to the obstruction of a toll-gate, have continued
serving but a small fraction of the use to the public that they
might serve ; but, on the abolition of the toll, and the substitution
of funds levied by taxation, instead of the charges collected per
drive or per walk across the bridge, the service afforded by the
bridge to the public has been vastly augmented, and yet the cost
to the public is in no way increased by this, but it is even dimi-
nished by the saving of the remuneration to the toll-collector for
his services, no longer needed. High fares on railways operate as
a hindrance to the public from receiving so much as they might
of the advantage rendered available by the original construction
of the bridges, tunnels, cuttings, embankments, and other parts of
the whole works of the line; yet, by preventing a person from
travelling, no part of the first cost will be saved, but he will suffer
the loss of whatever advantage the journey might have afforded
him. If part of the funds were levied by taxation, and another
part by fares or charges on passenger and goods traffic, the fares
and other charges might be so much reduced as to effect so great
an increase of the traffic as would allow of the amount to be
levied by taxation being kept very small, and very little burden-
some to the community, while the public would gain the triple
advantage of being permitted to make more use of the railways
already existing, while paying much less for each journey; and of
obtaining valuable railway accommodation in many localities to
which railways could not be profitably extended on the principle
of their being made and worked by companies. The results of the
elaborate investigations of the Royal Commissioners appointed to
inspect the accounts and examine the works of the railways in
Ireland, as embodied in their two reports, may lead us to look
in hope to the prospect of the railways of Ireland being soon

1867] WARMING AND VENTILATING 477

rendered public property, and with confidence that, in that event,
if the purchase be effected with due prudence, a vast benefit will
accrue to the general public in Ireland.

68. WARMING AND VENTILATING.

[Read before the Belfast Natural History and Philosophical Society, 4 Dec.
1867. From the MS. notes supplemented by a newspaper report.]

IF I had offered at the present season, and in the present
state of the weather, a paper on warming alone; I might reasonably
have anticipated a favourable reception from my audience. I know
however that many people shudder at the very thought of venti-
lation and I am conscious that it requires no small amount of
boldness to come forward, in a frosty beginning of December, to
advocate the introduction of fresh air into people's houses in any
other than in homeopathic doses. Knowing however, as I well do.
the great amount of discomfort, generally, and almost universally,
suffered in dwellings and other buildings from vitiated and over-
heated air, accompanied often by cold draughts along the floor,
or at other places in apartments; and knowing how those evils
may in general be mitigated, or altogether removed ; and by what
means pleasant and healthful air may be usually made available ;
I have determined to brave the opposition with which the ad-
vocacy of ventilation will assuredly be met in many of your minds.

Ventilation is not in reality the dreadful thing that it is often
supposed to be. It consists in the attainment of a due and proper
change of air in any apartment, passage, or other enclosed space to
which the external atmosphere has not free and unlimited access ;
and it is essential to good ventilation of places to be occupied by
people or other animals that the fresh air should be so introduced
as not to cause cold or discomfort to the occupants, but on the
contrary to render the place more healthful and more agreeable
for them to live in.

The principal cases for which means of ventilation are requisite,
are : — dwelling houses, public buildings, ships, factories, mines ; as
also stables, cow houses and the like.

It is only to a small portion of this wide range of cases that
my remarks on the present occasion must be confined.

478 APPENDIX [68

There are many varieties of methods for ventilation, and there
is no single one that can be regarded as the best for all cases;
but in arranging the method to be pursued in any particular
case, various circumstances may require to be taken into account,
such as

(1) The uses to which the apartments or spaces have to be
applied.

(2) The number of individuals commonly or occasionally
occupying them.

(3) The requirements and means for warming and lighting
them.

(4) The requirements for ventilation at different seasons of
the year.

The source of the motive power for producing ventilation is in
the vast majority of instances the ascent of heated air, whether
naturally or artificially produced. In hot weather, or in warm
climates, ventilation is often attained by the simple method of
opening windows or other apertures widely, and trusting to the
breezes, or yet more gentle motions, of the external atmosphere,
for the attainment of the requisite change of air. This may be
called natural ventilation ; and as the winds and breezes of the
atmosphere are due wholly to differences of temperature at
different parts of the earth and 'atmosphere, the change of air
even in this case is to be traced ultimately to the ascent of heated
masses of air.

In ordinary dwelling houses, fires burned for the primary
purpose of attaining warmth afford incidentally likewise a source
of motive power which is a most important means for promoting
ventilation.

The fires are constantly withdrawing by their chimneys the
air from the apartments, and the flow of air which may thence
be attained can easily be made by proper arrangements to suffice
in ordinary cases for very good ventilation. What is mainly re-
quired consists simply in the providing of properly formed and
properly placed apertures for the admission of air under the in-
drawing tendency of the heated chimney. This may usually be
advantageously effected by having a large aperture formed in a
wall of the room at a convenient place near the ceiling, and adapted
for receiving air from the hall, passage, or staircase, and by aid of
some guiding woodwork or other means adapted for shooting it

1867J WARMING AND VENTILATING 479

obliquely upwards quite to the ceiling, so that it may flow rapidly
along the ceiling in a broad but moderately thin sheet. The air,
when thus set into motion along the ceiling, although it is colder
and heavier than the air below, yet tends to cling to the ceiling,
and does not fall down through the warmer air as a current, nor
in large detached masses, but gradually mingles and unites with
the general air of the room in the space quite above the heads
of the occupants, so that no cold, unpleasant draughts are felt ; but
the air of the room is kept in a condition of agreeable freshness.

In connection with this, a great abatement of the usual cold
draughts flowing along the floor, or of the cold air stagnating
there, ensues or tends to ensue, and is rendered easily practicable.
Thus, if the air is admitted freely by a properly arranged venti-
lator, it will not rush in so briskly as before by chinks in the floor
or under the door. All such chinks, too, may then be carefully
closed by improved fittings ; while, if closed in the absence of a
ventilating inlet, the draught up the chimney would fail to be
sufficient, and the room would become smoky. The aperture in
the woodwork where the air issues into the room may be made
about two or three feet wide, as horizontally measured in a
direction parallel to the wall, and the width across may be made
variable at pleasure, but may very well be ordinarily in winter
kept at about two or three inches wide. The aperture through
the wall should be of greater area, so that it may not obstruct the
flow. On the outside of the wall — that is to say, the side next
the hall or staircase — there ought to be either louvres or some
other suitable screen for preventing persons outside of the room
from seeing into its upper part through the ventilator, and for
aiding in preventing the too free transmission of sound (as of the
speaking of persons within) through the ventilator.

Professor Thomson here exhibited and explained to the meeting
by aid of large drawings, the detailed arrangements of several
varieties of such ventilators which had been found good and
suitable in practice. In proof of the necessity of means for
attaining a more equable distribution of warmth in ordinary
dwelling apartments than is met with when no special provision
is made for that purpose, especially in rooms lighted by gas,
Professor Thomson cited some observations which he had made
on a winter evening in a room in his own house. The room had
no ventilator and was lighted by a pair of small gas burners, and

480 APPENDIX [68

a small fire was burning in the grate. The door of the room
having been shut for some time, he found the temperature, shown
by a thermometer placed a few inches above the floor, to be 56° F.;
while the temperature at the top of a bookcase a little below the
ceiling was 72°, and so the difference of temperature between
the floor and the ceiling was no less than 16° F. The door of the
room was then left wide open for an hour and a half, and the
temperatures were observed at the same two places, and found
to be, near the floor 52°, and near the ceiling 73°, so that the
difference now was increased to 21° and the keeping of the door
open had been quite ineffective in cooling the air of the apartment
near the ceiling. The air near the ceiling had, indeed, risen in
temperature by 1° during the hour and a half when the door was
left open. This was sufficient proof that no satisfactory ventilation
of a sitting-room with gas lights on a winter evening is attain-
able by widely opening the door. But, besides, it is to be
observed that, when the door is wide open, a cold current of air
flows in along the floor, while warm air passes outwards by
the upper part of the doorway, and thus people's feet are kept
cold by the fresh air, of which they get a very insufficient
supply to breathe. This can readily be observed by standing
in the open doorway of a warmed sitting-room, and holding a
burning taper in the hand at different heights successively, when
the blowing of the flame will show the motion of the air very
clearly and convincingly.

Professor Thomson mentioned the well-known ventilator intro-
duced by Dr Arnott, which is adapted for drawing into the chimney
hot and vitiated air from the upper part of the room. He did not,
however, much approve of the principle of that kind of ventilator,
because he preferred the principle of scouring out the heated air
from the upper part of the room by introducing the fresh air there.
He recommended strongly, however, the use, whenever practicable,
of chimney pipes for leading the products of combustion of the gas
flames to the chimney of the fireplace. These chimney pipes, on
account of danger of fire and for some other reasons, ought by no
means to be placed for concealment from view between the ceiling
of the apartment and the floor of the room above, but they ought
to be made ornamental, or as little unsightly as possible, and con-
ducted close below the ceiling without touching it, or in any other
suitable situation free from danger of setting fire to the house.

1867] WARMING AND VENTILATING 481

He mentioned several reasons for preferring to draw the fresh air
for apartments from the hall and other passages of the house
rather than directly from the external atmosphere, among which
were that the external air in towns often carries so much of sooty
particles — too well known as "blacks" — that it does not always
suit well for being introduced at once into apartments without
having first been allowed to get rid, in a great degree, of these
particles by depositing them in the passages, or in some little
used apartment through which the air may be drawn. One or
more windows or other apertures ought always to be kept open
to admit air to the staircase or other passages of the house. The
omission to do this is the usual cause of the back smoke coming
down the unused chimneys, which is a very common annoyance
in dwellings.

He explained some of the methods which he could most recom-
mend for warming the fresh supplies of air introduced into passages
of houses. The warming in a slight degree of the air while entering
the passages of the house, or while in them, is not usually to be
regarded as necessary, but may sometimes be desirable, especially
in very cold weather, or in case of persons liable to suffer much
from cold. Professor Thomson then, with the aid of drawings,
gave explanations of ordinary and frequent circumstances of the
warming and ventilating of public buildings. In doing so he
spoke in condemnation of methods depending on the introduction
of the fresh air, whether warm or cold, through the floor or by
any openings near the occupants; and recommended rather that
the fresh air be introduced near the ceiling, and well mixed with
the general atmosphere of the room before reaching the occupants ;
and that it should be introduced in quantity sufficient to maintain
a satisfactory degree of freshness in the whole space. Professor
Thomson had given much attention to the subject of th^ ventila-
tion of public buildings, and he offered various recommendations
and suggestions for improvements from prevailing practices. The
limits of the present abstract of the lecture, however, do not allow
more than the mention of this part of the subject, as it has
appeared that a greater number of the general public may be
practically interested in the means taught for improving the
comfort and healthfulness of their own dwellings.

An interesting discussion followed the reading of the paper,
in which several members took part.

T. 31

INDEX

Aberfoil Glacial markings 420
Anchor Ice, St Lawrence xxxv, 258
Andrews, Dr Thomas, conducts classes
for J. Thomson liv ; Bakerian Lecture
Ix; Testimonial from Ixix; Letters from
Ixxi; President of Brit. Assoc. Ixxiv;
On Continuity of States of Matter 278
et seq., 290 et seq., 308 ; Notes bearing
on Experiments 318 et seq.
Arago, F., On Anchor Ice 260
Atmospheric Circulation, Early con-
sideration of xxvi, xxxvi; Bakerian
Lecture on xc, 153; Papers on 144
Atmospheric Refraction of level Eays
Ixv, 441

Barlow, W. H., Correspondence on
Limits of Safety under varying stresses
404

Barnes, Prof. H. T., On Anchor Ice xxxv,
266

Barr, Prof. Archibald, Experiments on
Gauging by V notches xlv; On Fric-
tion Break Dynamometer xlvi; On
Law of Similar Structures Ixxi, 372;
becomes Thomson's successor in Glas-
gow Ixxxviii; On River-bend experi-
ments 106

Basalt, prismatic structure in xlii, Ixxv,
422

Beams of Light, Visual Appearance of
459

Bell, Alexander Graham, shows early
telephone in Glasgow Ixxv

Benard, Prof. H., Convective Circulation
in Liquids 136

Blackburn, Prof. Hugh, proposer of
honorary LL.D. Ixii

Blackburn, Mrs Hugh, drawings of birds,
&c. Ixiii

Bottomley, W., sen. xvi, xli, xlviii

Buch, L. von, On Atmospheric Circu-
lation 174

Cagniard de la Tour, transition from

liquid to gas 320
Caird, Dr John, appreciations by Ixxxix,

xci

Calm Lines on rippled Sea liii, 142
Carnot, Sadi xxxv, 196, 204
Centrifugal Pump xliii, Ixvii, 16

Christie, Prof. S. H., experiments show-
ing plasticity of ice 211

Clinure civ, 380 note

Continuity of States of Matter, ^npub-
lished notes 276, 318 ; Roy. Soc. 278,
307; Belfast Nat. Hist. Soc. 291; Brit.
Ass. 286, 297

Crum, Walter xviii, xxvii

Crystallization, influence of stresses on
xxxv, liv; Roy. Soc. paper 236; cor-
respondence with W. Thomson 245 ;
correspondence with H. C. Sorby 252 ;
later investigations 272

Cunningham, Capt. Allan, Hydraulic
experiments at Roorkee 112, 120

Dalton, John, On Trade Winds 168
D'Arcy and Bazin, experiments on flow-
ing water 109, 118 note
Darwin, Charles, on Parallel Roads of

Glen Roy 411
Daubeny, C. G. B., on Columnar Basalt

424

Demarara, centrifugal pump at 16
Design in creation xxxvii
Dimensional Equations, Brit. Assoc.

paper 375
Disintegration of earth by frost xxxvi,

269; of stones 257
Donny on change of state 280 note, 290,

329
Douglas, Robert, letters to, on design in

creation xxxvii ; on religious belief xl ;

fellow student at College Ixix note
Dove, Atmospheric Circulation 171, 173
Drennan, Dr William xv
Dufour, on change of state 280 note, 290
Dynamometer, friction break xlv, 24

Edgar, Dr Samuel, school at Bally-

nahinch xv
Elasticity, papers on xxxiv, 334, 341;

correspondence with W. H. Barlow

404

Ergometer, xlvi, 452 note
Everett, J. D. Ixvi note ; systems of units

375

Fairbairn, Sir W., pupilage with xxii,
Ixvi; his experiments on cast iron
336 note

INDEX

483

Faraday, M. xlix, liii; on plasticity of

ice 211, 222; on regelation 226, 230;

correspondence with, on regelation 212
Farquharson, Rev. James, on Anchor

Ice 261
Ferrel, W., on Atmospheric Circulation

174, 178, 185, 189
Flux and Reflux of Water 123
Fogs, on smoky 130, 133
Forbes, J. D., xxxiii, lii, Ixxxii, 205 note;

on plasticity of ice, etc. 208, 215, 218,

222, 230 407, 415
Francis, James B., his Lowell Hydraulic

Experiments 51, 80
Freezing Point, Lowering of, by Pressure

xxvi, xxxiv, xxxvi, 196, 204, 209
Froude, W., on "Vena Contracta" Ixxiv,

88
Fuller, George xlix, Ixxiii

Garden, Dr, on Atmospheric Circulation

158
Gauge Notch, V noteh for measuring

water xxvi, xliv; Brit. Ass. papers

1858 36; 1861 42; Table of Flow of

Water 54 ; Final paper, Brit. Assoc. 56
Giant's Causeway xlii, Ixxv; paper in

Glasg. Geolog. Soc. 422
Gibbs, J. Willard xxxv, 234 note, 244

note, 268 note, 276
Glacial Markings, paper to Brit. Assoc.

420

Gladstone, Dr J. H. Ixii
Glen Roy, Parallel Roads xxxiii, xxxvi ;

paper to Roy. Soc. Edinb. 407
Gordon, Prof. Lewis D. B. xxi, xxvii, xl,

Ixx
Gordon, Robert, Hydraulic Experiments

on Irrawaddy 113

Hadley, George, on Atmospheric Circu-
lation 154, 161, 173, 181

Halley, Edmund, on Atmospheric Circu-
lation 154, 159, 181

Hancock, John, on Local Government
Question in Ireland 473

Hancock, Dr W. Neilson xli, xlviii,
Iviii, Ixxxvi

Helmholtz, H. von Ixiii; testimonial
from Ixvii

Herschel, Sir J., on Smoky Fogs 131 ;
on Atmospheric Circulation 173, 175

Hodgkinson, W. E., on Elasticity 334
note, 336 note, 339, 405

Humphreys and Abbot, Hydraulics of
the Mississippi 109, 121

Ice, Anchor xxxv, 258; lowering of
freezing point of xxvi, xxxiv, xxxvi,
196, 204 ; plasticity of 208, 272

Inertia, Law of 379

Integrating Machine Ixxiii; Koy. Soc.
paper 452

Interface 65, 327, 424

Jack, Prof. W. xxxix, Ixxxvii

Jamaica, Centrifugal Pump at 16

Jet Pump xliii; papers to Brit. Assoc.

26, 27, 30, 34
Joule, James P. xxx, lii; testimonial

from Ixviii

King, Elizabeth xvi note, Ixii, Ixxix,

Ixxx
Krakatoa, volcanic eruption 192

Lister, Dr Martin, on Trade winds 155
Lyell, Sir Charles; on Anchor Ice 260;
on Columnar Basalt 424

McClean, John R. xx, xxvii, xxxviii

McConnel, J. C., Crystallization and
Liquefaction 272 note; Correspond-
ence with 273

Main, J. F., Plasticity of Ice Ixxxii, 272

Maury, M. F., on Atmospheric Circula-
tion 146, 175, 189

Maxwell, J. Clerk Ixxii; Tears of strong
wine 129 note ; continuity of states of
matter 276, 281 note, 332 note; on
Systems of units 375 ; on Atmospheric
Refraction 448 ; on Integrating Ma-
chine 453 ; Correspondence with 457

Mississippi, windings of rivers 102 ; flow
of water in 108, 109

Models of Curves of Liquid and Gaseous
States 276, 321

Murphy, J. J. xli, liv; Circulation of
the Atmosphere 180

Nationalization of Public Works xlii,

472
Natterer, experiments on compression

of gases 331, 332
Neeson, Carr's Glen experiments on

Gauge Notches 41, 43
Newton, Sir Isaac, on "Vena Contracta "

89, 90

Nichol, Prof. J. P. xix
Nichol, Prof. John xix, xxxviii, Ixx,

Ixxxix
Numeric Ixxvii, 376

Perry, Prof. John li

Piddington, on Atmospheric Circulation
173

Plasticity of Ice, Roy. Soc. paper 208 ;
later investigations 272

Poncelet, J. V. xxviii, xxix, xxxi, xxxii

Poncelet and Lebros, hydraulic experi-
ments 35, 50 note, 61 note

Poundal 66 note

Problem on Point Motions 389

Public Parks xli ; paper to Social En-
quiry Society, Belfast 464

Purser, Frederick Ixxvii note

Purser, Prof. John lix ; on Atmospheric
Refraction Ixv ; Correspondence with
Ixxvi, Ixxxviii, xci

484

INDEX

Railways, State Purchase of, xlii, 472
Rankine, Prof. W. J. Macquorn Ixvi,

334 note

Bedfield, on Whirlwinds 172
Begelation 212, 222 et seq., 230 et

seq.
Regime, Uniform, flow of water in Ixxxii,

106
Regnault, H. V., experiments on steam

305, 311, 312, 316
River Bends xxvi, xxxvi, 96, 100, 102,

124, 152
Roberts-Austen, W. Chandler 437

Safety in structures xxvi, Ixx, 349,

404
Scrope, G. Poulett, on Columnar Basalt

427

Similar Structures, comparison of 361
Smoky Fogs 130, 133
Sorby, H. C., Correspondence on Geo-
logical Effects of Pressure 252, 421

note
South Kensington Loan Exhibition Ixxiv,

276
Spiral Springs, Elasticity and Strength

of xxxiv, 341

Stokes, Sir G. G. 123 note, 276
Strength of Materials xxvi, xxxiv, 334,

404
Structure, Prismatic in basalt xlii, Ixxv,

422

Tait, Prof. P. G. Ixvi; testimonial from
Ixviii, 386 note, 389, 401, 451

Thermodynamic surface 276

Thomson, James, senr. xiv; removal to
Glasgow xvii ; death xxxviii

Thomson, James, birth xvii ; at Glasgow
University xviii; Summer in France
xix ; travels in Germany xix ; pupilage
at Millwall xxii; ill health xxiii;
religious views xxxvii, xl; settles in

Belfast xl ; marriage xlviii ; professor-
ship in Belfast xlviii ; professorship in
Glasgow Ixvi; political views Ixxxi;
failure of eyesight Ixxxvii ; death xci

Thomson, William, Lord Kelvin xvi
note, xvii, xxxiv, xxxvii, xlix, Hi, liii,
Ix, Ixiii, Ixvi, Ixix, Ixxiii, Ixxv, Ixxix,
Ixxxi note ; Correspondence with xxvi,
xxviii, xlix, 1, liv, Iv, Ixii, Ixxxii, 220,
245, 449

Thomson, Sir C. Wyville 221

Torque xlvii

Trade Winds 144, 156, 162, 169, 177,
181

"Triple Point" 287, 298, 307

Tubular Pores in Ice 220

Turbine, vortex xxvi et seq., xliiH2

Tyndall, John xlix, 211, 217, 219, 222

Uniform Regime, flow of water in Ixxxii,

106
Units, metric, Brit. Assoc. paper 372

V notches xxvi, xliv, 36, 42, 54, 56

Varley, C. 128

"Vena Contracta" Ixxiv, 88

Viscosity in Elasticity 404

Visual Appearance of Beams of Light

459
Vortex water wheel, see Turbine xxvi et

seq., xlii, 2

van der Waals, J. D. Ixxii, 276

On Warming and Ventilating Ix, 477

Weir Boards 35, 36

Whirlpool of Free Mobility xxvi, xlii, 1,

18, 104, 151
Whirlwinds and Waterspouts xc, 125,

148
Windings of Rivers xxvi, xxxvi, 96, 100,

102, 124, 152

Young, T. 125

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